NCERT Solutions for Class 7 Maths Chapter 5 Lines & Angles are provided here with simple step-by-step explanations. These solutions for Lines & Angles are extremely popular among class 7 students for Maths Lines & Angles Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of class 7 Maths Chapter 5 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NCERT Solutions. All NCERT Solutions for class 7 Maths are prepared by experts and are 100% accurate.
Page No 128:
Question 1:
In the given question, there are four options out of which one is correct. Write the correct one.
The angles between North and West and South and East are
(a) complementary
(b) supplementary
(c) both are acute
(d) both are obtuse
Answer:
ans
Page No 128:
Question 2:
In the given question, there are four options out of which one is correct. Write the correct one.
Angles between South and West and South and East are
(a) vertically opposite angles
(b) complementary angles
(c) making a linear pair
(d) adjacent but not supplementary
Answer:
ans
Page No 128:
Question 3:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ ABC = 46°, then ∠ ABP is equal to
(a) 44°
(b) 67°
(c) 13°
(d) 62°
Answer:
ans
Page No 129:
Question 4:
In the given question, there are four options out of which one is correct. Write the correct one.
If the complement of an angle is 79°, then the angle will be of
(a) 1°
(b) 11°
(c) 79°
(d) 101°
Answer:
ans
Page No 129:
Question 5:
In the given question, there are four options out of which one is correct. Write the correct one.
Angles which are both supplementary and vertically opposite are
(a) 95°, 85°
(b) 90°, 90°
(c) 100°, 80°
(d) 45°, 45°
Answer:
ans
Page No 129:
Question 6:
In the given question, there are four options out of which one is correct. Write the correct one.
The angle which makes a linear pair with an angle of 61° is of
(a) 29°
(b) 61°
(c) 122°
(d) 119°
Answer:
ans
Page No 129:
Question 7:
In the given question, there are four options out of which one is correct. Write the correct one.
The angles x and 90° – x are
(a) supplementary
(b) complementary
(c) vertically opposite
(d) making a linear pair
Answer:
ans
Page No 129:
Question 8:
In the given question, there are four options out of which one is correct. Write the correct one.
The angles x – 10° and 190° – x are
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
Answer:
ans
Page No 129:
Question 9:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, the value of x is
(a) 110°
(b) 46°
(c) 64°
(d) 150°
Answer:
ans
Page No 129:
Question 10:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, if AB || CD, ∠ APQ = 50° and ∠PRD = 130°, then ∠QPR is
(a) 130°
(b) 50°
(c) 80°
(d) 30°
Answer:
ans
Page No 130:
Question 11:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, lines l and m intersect each other at a point. Which of the following is false?
(a) ∠a = ∠b
(b) ∠d = ∠c
(c) ∠a + ∠d = 180°
(d) ∠a = ∠d
Answer:
ans
Page No 130:
Question 12:
In the given question, there are four options out of which one is correct. Write the correct one.
If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is
(a) 120°
(b) 60°
(c) 30°
(d) 20°
Answer:
ans
Page No 130:
Question 13:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, POR is a line. The value of a is
(a) 40°
(b) 45°
(c) 55°
(d) 60°
Answer:
ans
Page No 130:
Question 14:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, POQ is a line. If x = 30°, then ∠ QOR is
(a) 90°
(b) 30°
(c) 150°
(d) 60°
Answer:
ans
Page No 131:
Question 15:
In the given question, there are four options out of which one is correct. Write the correct one.
The measure of an angle which is four times its supplement is
(a) 36°
(b) 144°
(c) 16°
(d) 64°
Answer:
ans
Page No 131:
Question 16:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, the value of y is
(a) 30°
(b) 15°
(c) 20°
(d) 22.5°
Answer:
ans
Page No 131:
Question 17:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, PA || BC || DT and AB || DC. Then, the values of a and b are respectively.
(a) 60°, 120°
(b) 50°,130°
(c) 70°,110°
(d) 80°,100°
Answer:
ans
Page No 131:
Question 18:
In the given question, there are four options out of which one is correct. Write the correct one.
The difference of two complementary angles is 30°. Then, the angles are
(a) 60°, 30°
(b) 70°, 40°
(c) 20°,50°
(d) 105°,75°
Answer:
ans
Page No 131:
Question 19:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, PQ || SR and SP || RQ. Then, angles a and b are respectively
(a) 20°, 50°
(b) 50°, 20°
(c) 30°,50°
(d) 45°, 35°
Answer:
ans
Page No 131:
Question 20:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, a and b are
(a) alternate exterior angles
(b) corresponding angles
(c) alternate interior angles
(d) vertically opposite angles
Answer:
ans
Page No 131:
Question 21:
In the given question, there are four options out of which one is correct. Write the correct one.
If two supplementary angles are in the ratio 1 : 2, then the bigger angle is
(a) 120°
(b) 125°
(c) 110°
(d) 90°
Answer:
ans
Page No 132:
Question 22:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠ QOS measures
(a) 150°
(b) 75°
(c) 45°
(d) 60°
Answer:
ans
Page No 132:
Question 23:
In the given question, there are four options out of which one is correct. Write the correct one.
Statements a and b are as given below:
a : If two lines intersect, then the vertically opposite angles are equal.
b : If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°.
Then
(a) Both a and b are true
(b) a is true and b is false
(c) a is false and b is true
(d) both a and b are false
Answer:
ans
Page No 132:
Question 24:
In the given question, there are four options out of which one is correct. Write the correct one.
For In the given figure, statements p and q are given below:
p : a and b are forming a linear pair.
q : a and b are forming a pair of adjacent angles. Then,
(a) both p and q are true
(b) p is true and q is false
(c) p is false and q is true
(d) both p and q are false
Answer:
ans
Page No 133:
Question 25:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, ∠AOC and ∠BOC form a pair of
(a) vertically opposite angles
(b) complementary angles
(c) alternate interior angles
(d) supplementary angles
Answer:
ans
Page No 133:
Question 26:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, the value of a is
(a) 20°
(b) 15°
(c) 5°
(d) 10°
Answer:
ans
Page No 133:
Question 27:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, if QP || SR, the value of a is
(a) 40°
(b) 30°
(c) 90°
(d) 80°
Answer:
ans
Page No 133:
Question 28:
In the given question, there are four options out of which one is correct. Write the correct one.
In which of the following figures, a and b are forming a pair of adjacent angles?
Answer:
ans
Page No 134:
Question 29:
In the given question, there are four options out of which one is correct. Write the correct one.
In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays
Then
(a) All (i), (ii) and (iii) are true
(b) (iii) is false
(c) (i) is false but (ii) and (iii) are true
(d) (ii) is false
Answer:
ans
Page No 134:
Question 30:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to
(a) 126°
(b) 144°
(c) 136°
(d) 154°
Answer:
ans
Page No 135:
Question 31:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, POQ is a line, then a is equal to
(a) 35°
(b) 100°
(c) 80°
(d) 135°
Answer:
ans
Page No 135:
Question 32:
In the given question, there are four options out of which one is correct. Write the correct one.
Vertically opposite angles are always
(a) supplementary
(b) complementary
(c) adjacent
(d) equal
Answer:
ans
Page No 135:
Question 33:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, a = 40°. The value of b is
(a) 20°
(b) 24°
(c) 36°
(d) 120°
Answer:
ans
Page No 135:
Question 34:
In the given question, there are four options out of which one is correct. Write the correct one.
If an angle is 60° less than two times of its supplement, then the greater angle is
(a) 100°
(b) 80°
(c) 60°
(d) 120°
Answer:
ans
Page No 135:
Question 35:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)°, then the measure of ∠2 in terms of b is
(a) (2 + b)°
(b) (3 – b)°
(c) (108 – b)°
(d) (180 – b)°
Answer:
ans
Page No 135:
Question 36:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, PQ||RS and a : b = 3 : 2. Then, f is equal to
(a) 36°
(b) 108°
(c) 72°
(d) 144°
Answer:
ans
Page No 136:
Question 37:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, line l intersects two parallel lines PQ and RS. Then, which one of the following is not true?
(a) ∠1 = ∠3
(b) ∠2 = ∠4
(c) ∠6 = ∠7
(d) ∠4 = ∠8
Answer:
ans
Page No 136:
Question 38:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, which one of the following is not true?
(a) ∠1 + ∠5 = 180°
(b) ∠2 + ∠5 = 180°
(c) ∠3 + ∠8 = 180°
(d) ∠2 + ∠3 = 180°
Answer:
ans
Page No 136:
Question 39:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure which of the following is true?
(a) ∠1 = ∠5
(b) ∠4 = ∠8
(c) ∠5 = ∠8
(d) ∠3 = ∠7
Answer:
ans
Page No 136:
Question 40:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, PQ||ST. Then, the value of x + y is
(a) 125°
(b) 135°
(c) 145°
(d) 120°
Answer:
ans
Page No 137:
Question 41:
In the given question, there are four options out of which one is correct. Write the correct one.
In the given figure, if PQ||RS and QR||TS, then the value a is
(a) 95°
(b) 90°
(c) 85°
(d) 75°
Answer:
ans
Page No 137:
Question 42:
Fill in the blanks to make the statement true.
If sum of measures of two angles is 90°, then the angles are _________.
Answer:
ans
Page No 137:
Question 43:
Fill in the blanks to make the statement true.
If the sum of measures of two angles is 180°, then they are _________.
Answer:
ans
Page No 137:
Question 44:
Fill in the blanks to make the statement true.
A transversal intersects two or more than two lines at _________ points.
Answer:
ans
Page No 137:
Question 45:
Fill in the blanks to make the statement true.
sum of interior angles on the same side of a transversal is____________ .
Answer:
ans
Page No 137:
Question 46:
If a transversal intersects two parallel lines, then
alternate interior angles have one common _________.
Answer:
ans
Page No 137:
Question 47:
If a transversal intersects two parallel lines, then
corresponding angles are on the__________ side of the transversal.
Answer:
ans
Page No 137:
Question 48:
If a transversal intersects two parallel lines, then
alternate interior angles are on the ___________ side of the transversal.
Answer:
ans
Page No 137:
Question 49:
Fill in the blanks to make the statement true.
Two lines in a plane which do not meet at a point anywhere are called _____________ lines.
Answer:
ans
Page No 137:
Question 50:
Fill in the blanks to make the statement true.
Two angles forming a __________ pair are supplementary
Answer:
ans
Page No 137:
Question 51:
Fill in the blanks to make the statement true.
The supplement of an acute is always __________ angle.
Answer:
ans
Page No 137:
Question 52:
Fill in the blanks to make the statement true.
The supplement of a right angle is always _________ angle.
Answer:
ans
Page No 137:
Question 53:
Fill in the blanks to make the statement true.
The supplement of an obtuse angle is always _________ angle.
Answer:
ans
Page No 137:
Question 54:
Fill in the blanks to make the statement true.
In a pair of complementary angles, each angle cannot be more than _________90°.
Answer:
ans
Page No 137:
Question 55:
Fill in the blanks to make the statement true.
An angle is 45°. Its complementary angle will be __________ .
Answer:
ans
Page No 137:
Question 56:
Fill in the blanks to make the statement true.
An angle which is half of its supplement is of __________.
Answer:
ans
Page No 137:
Question 57:
State whether the statement is True or False.
Two right angles are complementary to each other.
Answer:
ans
Page No 138:
Question 58:
State whether the statement is True or False.
One obtuse angle and one acute angle can make a pair of complementary angles.
Answer:
ans
Page No 138:
Question 59:
State whether the statement is True or False.
Two supplementary angles are always obtuse angles.
Answer:
ans
Page No 138:
Question 60:
State whether the statement is True or False.
Two right angles are always supplementary to each other.
Answer:
ans
Page No 138:
Question 61:
State whether the statement is True or False.
One obtuse angle and one acute angle can make a pair of suplementary angles.
Answer:
True
Page No 138:
Question 62:
State whether the statement is True or False.
Both angles of a pair of supplementary angles can never be acute angles.
Answer:
True
Page No 138:
Question 63:
State whether the statement is True or False.
Two supplementary angles always form a linear pair.
Answer:
True
Page No 138:
Question 64:
State whether the statement is True or False.
Two angles making a linear pair are always supplementary.
Answer:
True
Page No 138:
Question 65:
State whether the statement is True or False.
Two angles making a linear pair are always adjacent angles.
Answer:
True
Page No 138:
Question 66:
State whether the statement is True or False.
Vertically opposite angles form a linear pair.
Answer:
False
As vertically opposite angles are always equal but do not form a linear pair.
Page No 138:
Question 67:
State whether the statement is True or False.
Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles.
Answer:
False
As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles.
Page No 138:
Question 68:
State whether the statement is True or False.
Vertically opposite angles are either both acute angles or both obtuse angles.
Answer:
True
Page No 138:
Question 69:
State whether the statement is True or False.
A linear pair may have two acute angles.
Answer:
False
As a linear pair has one acute angle and one obtuse angle.
Page No 138:
Question 70:
State whether the statement is True or False.
An angle is more than 45°. Its complementary angle must be less than 45°.
Answer:
True
Let A and B are two angles making a complementary angle pair and A is greater than 45°.
A + B = 90°
⇒ B = 90° – A
Therefore, B will be less than 45°.
Page No 138:
Question 71:
State whether the statement is True or False.
Two adjacent angles always form a linear pair.
Answer:
False
As if both adjacent angles are acute angles, then they do not form a linear pair.
Page No 138:
Question 72:
Write down each pair of adjacent angles shown in the following figures:
(i)
(ii)
(iii)
(iv)
Answer:
(i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles.
(ii) ∠PQT and ∠PQR; ∠ORU and ∠QRP; ∠RPS and ∠RPQ are adjacent angles.
(iii) ∠TSV and ∠USV; ∠SVT and ∠SVU are adjacent angles.
(iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles.
Page No 139:
Question 73:
In each of the following figures, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.
(i)
(ii)
(iii)
(iv)
Answer:
(i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles.
∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4; ∠5 and ∠6; ∠5 and ∠8; ∠6 and ∠7; ∠7 and ∠8 are linear pairs.
(ii) There is no pair of vertically opposite angles.
∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs.
(iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair.
(iv) ∠POR and ∠QOS; ∠ROQ and ∠POS are two pairs of vertically opposite angles.
∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs.
Page No 139:
Question 74:
Name the pairs of supplementary angles in the following figures:
(i)
(ii)
(iii)
Answer:
(i) ∠AOD and ∠DOB; ∠DOB and ∠BOC, ∠BOC and ∠AOC; ∠AOC and ∠AOD are four pairs of supplementary angles.
(ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles.
(iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles.
Page No 140:
Question 75:
In the given figure, PQ || RS, TR || QU and ∠PTR = 42°. Find ∠QUR.
Answer:
Since, PQ || RS and TR is a transversal.
∴ ∠PTR – ∠TRU= 42° .....(1) (Alternate interior angles)
Also, TR || QU and RS is a transversal.
∴ ∠TRU + ∠QUR = 180° (Co-interior angles)
⇒ 42° + ∠QUR = 180° [From (1)]
⇒ ∠QUR = 180° – 42° = 138°
Page No 140:
Question 76:
The drawings below, show angles formed by the goalposts at different positions of a football player. The greater the angle, the better chance the player has of scoring a goal. For example, the player has a better chance of scoring a goal from Position A than from Position B.
(i)
(ii)
(iii)
In Parts (a) and (b) given below it may help to trace the diagrams and draw and measure angles.
(a) Seven football players are practicing their kicks. They are lined up in a straight line in front of the goalpost [Fig.(ii)]. Which player has the best (the greatest) kicking angle?
(b) Now the players are lined up as shown in Fig. (iii). Which player has the best kicking angle?
(c) Estimate at least two situations such that the angles formed by different positions of two players are complement to each other.
Answer:
(a) 4th player has the greatest kicking angle. So, this player has the best kicking angle.
(b) 4th player has the greatest kicking angle. So, this player has the best kicking angle.
(c) (45°, 45°) and (60°, 30°) are the two pairs of angles formed by different positions of two players such that they are complementary to each other.
(∵ 45° + 45° = 90° and 60° + 30°= 90°).
Page No 140:
Question 77:
The sum of two vertically opposite angles is 166°. Find each of the angles.
Answer:
Since vertically opposite angles are equal.
Let each angle be x.
According to the question,
x + x = 166°
⇒ 2x = 166°
Thus, both angles are 83°.
Page No 141:
Question 78:
In the given figure, l ||m||n. ∠ QPS = 35° and ∠ QRT = 55°. Find ∠PQR.
Answer:
We have,
l || m and PQ is a transversal
∴ ∠SPQ = ∠PQU (Alternate interior angles)
⇒ ∠PQU = 35° .....(1)
Also, m || n and QR is a transversal.
∴ ∠QRT = ∠RQU (Alternate interior angles)
⇒ ∠RQU = 35° .....(2)
Now, ∠PQR = ∠PQU + ∠UQR
= 35° + 55° [Using (1) & (2)]
= 90°
Page No 141:
Question 79:
In the given figure, P, Q and R are collinear points and TQ ⊥ PR,
Name; (a) pair of complementary angles
(b) two pairs of supplementary angles.
(c) four pairs of adjacent angles.
Answer:
(a) ∠TOS and ∠SQR is a pair of complementary angles.
(b) ∠PQT and ∠TOR; ∠SQR and ∠PQS are two pairs of supplementary angles.
(c) ∠PQT and ∠TQS; ∠TQS and SQR; ∠PQT and ∠TOR; ∠PQS and ∠SQR are four pairs of adjacent angles.
Page No 141:
Question 80:
In the given figure, OR ⊥ OP.
(i) Name all the pairs of adjacent angles.
(ii) Name all the pairs of complementary angles.
Answer:
(i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles.
(ii) ∠x and ∠y are complementary angles. If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles.
Page No 141:
Question 81:
If two angles have a common vertex and their arms form opposite rays, Then,
(a) how many angles are formed?
(b) how many types of angles are formed?
(c) write all the pairs of vertically opposite angles.
Answer:
(a) 13 angles are formed.
(b) 4 types of angles are formed i.e., vertically opposite angles, adjacent angles, supplementary angles and linear pairs.
(c) ∠1 and ∠3; ∠2 and ∠4 are the two pairs of vertically opposite angles.
Page No 141:
Question 82:
In the given figure are the following pairs of angles adjacent? Justify your answer.
Answer:
(i) Yes, and b are the adjacent angles as they have a common vertex, one common arm and other non-common arms on the opposite side of the common arm.
(ii) No, a and b are not adjacent angles as they don’t have common arm.
(iii) No, a and b are not adjacent angles as they don’t have common vertex.
(iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm.
Page No 142:
Question 83:
In the given figure, write all the pairs of supplementary angles.
Answer:
∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles.
Page No 142:
Question 84:
What is the type of other angle of a linear pair if
(a) one of its angle is acute?
(b) one of its angles is obtuse?
(c) one of its angles is right?
Answer:
(a) If one of the angles is acute, then other angle of a linear pair is obtuse.
(b) If one of the angles is obtuse, then other angle of a linear pair is acute.
(c) If one of the angles is right, then other angle of a linear pair is also right.
Page No 142:
Question 85:
Can two acute angles form a pair of supplementary angles? Give reason in support of your answer.
Answer:
No, two acute angles cannot form a pair of supplementary angles. As if both angles are 89° and 89°, even then they cannot make the sum 180°.
Page No 142:
Question 86:
Two lines AB and CD intersect at O . Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only.
Answer:
∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4 are four pairs of adjacent angles.
Page No 143:
Question 87:
If the complement of an angle is 62°, then find its supplement.
Answer:
ans
Page No 143:
Question 88:
A road crosses a railway line at an angle of 30° as shown in the given figure. Find the values of a, b and c.
Answer:
Since, l || m and q is a transversal
∴ ∠1 = 30° .....(1) (Corresponding angles)
Also, m is a straight line.
∴ ∠b + ∠1 = 180° (Linear pair)
⇒ ∠b = 180° – 30° = 150° [Using (1)]
Now, p || q and m is a transversal.
∴ ∠1 = ∠3 = 30° .....(2) (Corresponding angles)
∠a = ∠3 [Vertically opposite angles]
∴ ∠a = 30° [Using (2)]
Also, p || q and l is a transversal.
∴ ∠2 = 30° (Corresponding angles)
Now, l is a straight line.
∴ ∠c + ∠2 = 180° [Linear pair]
⇒ ∠c + 30° = 180° [Using (iii)]
⇒ ∠c = 180° – 30° = 150°
Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°
Page No 144:
Question 89:
The legs of a stool make an angle of 35° with the floor as shown in the given figure. Find the angles x and y.
Answer:
l || m and QR is a transversal.
∴ ∠x = 35° (Alternate interior angles)
and ∠y + 35° = 180° (Co-interior angles)
⇒ ∠y = 180° – 35° = 145°
Hence, ∠x = 35° and ∠y = 145°.
Page No 144:
Question 90:
Iron rods a, b, c, d, e and f are making a design in a bridge as shown in the given figure, in which a ||b, c ||d, e || f. Find the marked angles between
(i) b and c
(ii) d and e
(iii) d and f
(iv) c and f
Answer:
(i) Let the angle between b and c is ∠1. and ∠1 = 30°[Vertically opposite angles]
(ii) Let the angle between d and e is ∠2.
Now, c || d and e is a transversal.
∴ ∠2 + 75° = 180° (Co-interior angles)
⇒ ∠2 = 180° – 75° = 105°
(iii) Let the angle between d and f is ∠3.
Now, e || f and d is a transversal.
∴ ∠2 + 3 = 180° (Co-interior angles)
⇒ ∠3 – 180° – 105° = 75° [From (ii) part]
(iv) Let the angle between c and f is ∠4.
Now, e || f and c is a transversal.
∴ ∠4 = 75° (Alternate interior angles]
Page No 144:
Question 91:
Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in the given figure and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.
Answer:
∠1 = 120° .....(1) (Vertically opposite angles)
c || f and a is transversal.
∴ ∠1 + ∠x = 180° (Co-interior angles)
⇒ 120° + ∠x – 180° [Using (1)]
⇒ ∠x = 180° – 120° = 60°
Now, a || d and c is a transversal.
⇒ ∠x + ∠2 = 180° (Co-interior angles)
⇒ 60° + ∠2 = 180° [Using (ii)]
⇒ ∠2 = 180° − 60° = 120°
⇒ ∠2 = ∠y = 120° (Vertically opposite angles)
Also, a || d and f is a transversal.
∴ ∠1 + ∠z = 180° (Co-interior angles)
⇒ 120° + ∠z = 180° [Using (i)]
⇒ ∠z = 180° – 120° = 60°
Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°
Page No 145:
Question 92:
In the given figure, AB||CD, AF||ED, ∠AFC = 68° and ∠FED = 42°. Find ∠EFD.
Answer:
Since AF || ED and FD is a transversal.
∴ ∠3 = 68° .....(1) (Corresponding angles)
Now, AB || CD and ED is a transversal.
∴ (∠2+42°) + ∠3 = 180° (Co-interior angles)
⇒ ∠2 = 180° – 42° – 68° [Using (1)]
⇒ ∠2 = 70° .....(2)
Also, AB || CD and EF is a transversal.
∴ ∠1 = ∠2 (Alternate interior angles)
⇒ ∠1 = 70° [Using (2)]
Thus, ∠EFD = 70°
Page No 145:
Question 93:
In the given figure, OB is perpendicular to OA and ∠BOC = 49°. Find ∠AOD.
Answer:
Given that ∠AOB = 90° (∵ OB ⊥ OA)
⇒ ∠BOC + ∠COA = 90°
⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)]
⇒ ∠COA – 41° .....(1)
Now, CD is a straight line.
∴ ∠AOD + ∠AOC = 180° [Linear pair]
⇒ ∠AOD = 180° − 41° [Using (1)]
∴ ∠AOD = 139°
Page No 145:
Question 94:
Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° , find ∠COF.
Answer:
ans
Page No 145:
Question 95:
Measures (in degrees) of two complementary angles are two consecutive even integers. Find the angles.
Answer:
ans
Page No 145:
Question 96:
If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles.
Answer:
ans
Page No 146:
Question 97:
Two angles are making a linear pair. If one of them is one-third of the other, find the angles.
Answer:
ans
Page No 146:
Question 98:
Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.
Answer:
ans
Page No 146:
Question 99:
In the given figure, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.
Answer:
ans
Page No 146:
Question 100:
In the given figure, find the value of ∠BOC, if points A, O and B are collinear.
Answer:
ans
Page No 146:
Question 101:
In the given figure, if l ||m, find the values of a and b.
Answer:
ans
Page No 147:
Question 102:
In the given figure, l ||m and a line t intersects these lines at P and Q, respectively. Find the sum 2a + b.
Answer:
ans
Page No 147:
Question 103:
In the given figure, QP || RS. Find the values of a and b.
Answer:
ans
Page No 147:
Question 104:
In the given figure, PQ || RT. Find the value of a + b.
Answer:
ans
Page No 147:
Question 105:
In the given figure, PQ, RS and UT are parallel lines.
(i) If c = 57o and a = , find the value of d.
(ii) If c = 75o and a =c, find b.
Answer:
ans
Page No 148:
Question 106:
In the given figure, AB||CD . Find the reflex ∠ EFG.
Answer:
ans
Page No 148:
Question 107:
In the given figure, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y.
Answer:
ans
Page No 148:
Question 108:
In the given figure, l, m and n are parallel lines, and the lines p and q are also parallel. Find the values of a, b and c.
Answer:
ans
Page No 149:
Question 109:
In the given figure, state which pair of lines are parallel. Give reason.
Answer:
ans
Page No 149:
Question 110:
In the given figure, examine whether the following pairs of lines are parallel or not:
(i) EF and GH (ii) AB and CD
Answer:
ans
Page No 149:
Question 111:
In the given figure, find out which pair of lines are parallel:
Answer:
ans
Page No 150:
Question 112:
In the given figure, show that
(i) AB || CD
(ii) EF || GH
Answer:
ans
Page No 150:
Question 113:
In the given figure, two parallel lines l and m are cut by two transversals p and q. Determine the values of x and y
Answer:
ans
View NCERT Solutions for all chapters of Class 7