Rs Aggarwal 2018 Solutions for Class 7 Math Chapter 17 Constructions are provided here with simple step-by-step explanations. These solutions for Constructions are extremely popular among Class 7 students for Math Constructions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 7 Math Chapter 17 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.
Page No 204:
Question 1:
Draw a line AB and take a point P outside it. Draw a line CD parallel to AB and passing through the point P.
Answer:
Page No 204:
Question 2:
Draw a line AB and draw another line CD parallel to AB at a distance of 3.5 cm from it.
Answer:
Page No 204:
Question 3:
Draw a line l and draw another line m parllel to l at a distance of 4.3 cm from it.
Answer:
Page No 207:
Question 1:
Construct a ∆ABC in which BC = 3.6 cm, AB = 5 cm and AC = 5.4 cm. Draw the perpendicular bisector of the side BC.
Answer:
Page No 207:
Question 2:
Construct a ∆PQR in which QR = 6 cm, PQ = 4.4 cm and PR = 5.3 cm. Draw the bisector of ∠P.
Answer:
Page No 207:
Question 3:
Construct an equilateral triangle each of whose sides measures 6.2 cm. Measure each of its angles.
Answer:
When we will measure angles of triangle using protractor then we find that all angles are equal to 60
Page No 207:
Question 4:
Construct a ∆ABC in which AB = AC = 4.8 cm and BC = 5.3 cm. Measure ∠B and ∠C. Draw AD ⊥ BC.
Answer:
Page No 207:
Question 5:
Construct a ∆ABC in which AB = 3.8 cm, ∠A = 60° and AC = 5 cm.
Answer:
Page No 208:
Question 6:
Construct a ∆ABC in which BC = 4.3 cm, ∠C = 45° and AC = 6 cm.
Answer:
Page No 208:
Question 7:
Construct a ∆ABC in which AB = AC = 5.2 cm and ∠A = 120°. Draw AD ⊥ BC.
Answer:
Page No 208:
Question 8:
Construct a ∆ABC in which BC = 6.2 cm, ∠B = 60° and ∠C = 45°.
Answer:
Page No 208:
Question 9:
Construct a ∆ABC in which BC = 5.8 cm, ∠B = ∠C = 30°. Measure AB and AC. What do you observe?
Answer:
Page No 208:
Question 10:
Construct a ∆ABC in which AB = 7 cm, ∠A = 45° and ∠C = 75°.
Answer:
Page No 208:
Question 11:
Construct a ∆ABC in which BC = 4.8 cm, ∠C = 90° and AB = 6.3 cm.
Answer:
Page No 208:
Question 12:
Construct a right-angled triangle one side of which measures 3.5 cm and the length of whose hypotenuse is 6 cm.
Answer:
Page No 208:
Question 13:
Construct a right triangle having hypotenuse of length 5.6 cm and one of whose acute angles measures 30°.
Answer:
Page No 208:
Question 1:
Mark (✓) against the correct answer
The supplement of 45° is
(a) 45°
(b) 75°
(c) 135°
(d) 155°
Answer:
Page No 208:
Question 2:
Mark (✓) against the correct answer
The complement of 80° is
(a) 100°
(b) 10°
(c) 20°
(d) 280°
Answer:
Page No 208:
Question 3:
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An angle is its own complement. The measure of the angle is
(a) 30°
(b) 45°
(c) 90°
(d) 60°
Answer:
Page No 208:
Question 4:
Mark (✓) against the correct answer
An angle is one-fifth of its supplement. The measure of the angle is
(a) 30°
(b) 15°
(c) 75°
(d) 150°
Answer:
Page No 208:
Question 5:
Mark (✓) against the correct answer
An angle is 24° more than its complement. The measure of the angle is
(a) 47°
(b) 57°
(c) 53°
(d) 66°
Answer:
Page No 208:
Question 6:
Mark (✓) against the correct answer
An angle is 32° less than its supplement. The measure of the angle is
(a) 37°
(b) 74°
(c) 148°
(d) none of these
Answer:
Page No 208:
Question 7:
Mark (✓) against the correct answer
Two supplementary angles are in the ratio 3 : 2. The smaller angle measures
(a) 108°
(b) 81°
(c) 72°
(d) none of these
Answer:
Page No 208:
Question 8:
Mark (✓) against the correct answer
In the given figure, AOB is a straight line and the ray OC stands on it.
If ∠BOC = 132°, then ∠AOC = ?
(a) 68°
(b) 48°
(c) 42°
(d) none of these
Answer:
Page No 208:
Question 9:
Mark (✓) against the correct answer
In the given figure, AOB is a straight line, ∠AOC = 68° and ∠BOC = x°.
The value of x is
(a) 32
(b) 22
(c) 112
(d) 132
Answer:
Page No 208:
Question 10:
Mark (✓) against the correct answer
In the adjoining figure, what value of x will make AOB a straight line?
(a) x = 30
(b) x = 35
(c) x = 25
(d) x = 40
Answer:
Page No 209:
Question 11:
Mark (✓) against the correct answer
In the given figure, what value of x will make AOB a straight line?
(a) x = 50
(b) x = 100
(c) x = 60
(d) x = 80
Answer:
Page No 209:
Question 12:
Mark (✓) against the correct answer
In the given figure, it is given that AOB is a straight line and 4x = 5y.
What is the value of x?
(a) 100
(b) 105
(c) 110
(d) 115
Answer:
Page No 209:
Question 13:
Mark (✓) against the correct answer
In the given figure, two straight lines AB and CD intersect at a point O and ∠AOC = 50°. Then, ∠BOD = ?
(a) 40°
(b) 50°
(c) 130°
(d) 60°
Answer:
Page No 209:
Question 14:
Mark (✓) against the correct answer
In the given figure, AOB is a straignt line, ∠AOC = (13x − 8)°, ∠COD = 50° and ∠BOD = (x + 10)°. The value of x is
(a) 32
(b) 42
(c) 36
(d) 52
Answer:
Page No 209:
Question 15:
Mark (✓) against the correct answer
In ∆ABC, side BC has been produced to D. If ∠ACD = 132° and ∠A = 54°, then ∠B = ?
(a) 48°
(b) 78°
(c) 68°
(d) 58°
Answer:
Page No 209:
Question 16:
Mark (✓) against the correct answer
In ∆ABC, side BC has been produced to D. If ∠BAC = 45° and ∠ABC = 55°, then ∠ACD = ?
(a) 80°
(b) 90°
(c) 100°
(d) 110°
Answer:
Page No 209:
Question 17:
Mark (✓) against the correct answer
In the given figure, side BC of ∆ABC is produced to D such that ∠ABC = 70° and ∠ACD = 120°. Then, ∠BAC = ?
(a) 60°
(b) 50°
(c) 70°
(d) 35°
Answer:
Page No 209:
Question 18:
Mark (✓) against the correct answer
In the given figure, rays OA, OB, OC and OD are such that ∠AOB = 50°, ∠BOC = 90°, ∠COD = 70° and ∠AOD = x°.
Then, the value of x is
(a) 50°
(b) 70°
(c) 150°
(d) 90°
Answer:
Page No 209:
Question 19:
Mark (✓) against the correct answer
In the given figure, ∠A = 50°, CE || BA and ∠ECD = 60°
Then, ∠ACB = ?
(a) 50°
(b) 60°
(c) 70°
(d) 80°
Answer:
Page No 209:
Question 20:
Mark (✓) against the correct answer
In ∆ABC, if ∠A = 65° and ∠C = 85°, then ∠B = ?
(a) 25°
(b) 30°
(c) 35°
(d) 40°
Answer:
Page No 209:
Question 21:
Mark (✓) against the correct answer
The sum of all angles of a triangle is
(a) 90°
(b) 100°
(c) 150°
(d) 180°
Answer:
Page No 210:
Question 22:
Mark (✓) against the correct answer
The sum of all angles of a quadrilateral is
(a) 180°
(b) 270°
(c) 360°
(d) 480°
Answer:
Page No 210:
Question 23:
Mark (✓) against the correct answer
In the given figure, AB || CD. ∠OAB = 150° and ∠OCD = 120°.
Then ∠AOC = ?
(a) 80°
(b) 90°
(c) 70°
(d) 100°
Answer:
Page No 210:
Question 24:
Mark (✓) against the correct answer
In the given figure, PQ || RS. ∠PAB = 60° and ∠ACS = 100°.
Then ∠BAC = ?
(a) 40°
(b) 60°
(c) 80°
(d) 50°
Answer:
Page No 210:
Question 25:
Mark (✓) against the correct answer
In the given figure, AB || CD || EF, ∠ABG = 110°, ∠GCD = 100° and ∠BGC = x°.
Then x = ?
(a) 35
(b) 50
(c) 30
(d) 40
Answer:
Page No 210:
Question 26:
The sum of any two sides of a triangle is always
(a) equal to the third side
(b) less than the third side
(c) greater than or equal to the 3rd side
(d) greater than the 3rd side
Answer:
Page No 210:
Question 27:
The diagonals of a rhombus
(a) are always equal
(b) never bisect each other
(c) always bisect each other at an acute angle
(d) always bisect each other at right angles
Answer:
Page No 210:
Question 28:
Mark (✓) against the correct answer
In ∆ABC, ∠B = 90°, AB = 5 cm and AC = 13 cm. Then, BC = ?
(a) 8 cm
(b) 18 cm
(c) 12 cm
(d) none of these
Answer:
Page No 210:
Question 29:
Mark (✓) against the correct answer
In a ∆ABC, it is given that ∠B = 37°, and ∠C = 29°. Then, ∠A = ?
(a) 86°
(b) 66°
(c) 114°
(d) 57°
Answer:
Page No 210:
Question 30:
Mark (✓) against the correct answer
The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the largest angle is
(a) 84°
(b) 98°
(c) 105°
(d) 91°
Answer:
Page No 210:
Question 31:
Mark (✓) against the correct answer
In a ∆ABC, if 2∠A = 3∠B = 6∠C, then ∠B = ?
(a) 30°
(b) 90°
(c) 60°
(d) 45°
Answer:
Page No 210:
Question 32:
Mark (✓) against the correct answer
In a ∆ABC, if ∠A + ∠B = 65° and ∠B +∠C = 140°. Then, = ∠B?
(a) 25°
(b) 35°
(c) 40°
(d) 45°
Answer:
Page No 210:
Question 33:
Mark (✓) against the correct answer
In a ∆ABC, ∠A − ∠B = 33° and ∠B −∠C = 18°. Then, = ∠B?
(a) 35°
(b) 55°
(c) 45°
(d) 57°
Answer:
Page No 211:
Question 34:
Mark (✓) against the correct answer
The angles of a triangle are (3x)° ,(2x − 7)° and (4x − 11)°. Then, x = ?
(a) 18
(b) 20
(c) 22
(d) 30
Answer:
Page No 211:
Question 35:
Mark (✓) against the correct answer
∆ABC is right-angled at A. If AB = 24 cm and AC = 7 cm then BC = ?
(a) 31 cm
(b) 17 cm
(c) 25 cm
(d) 28 cm
Answer:
Page No 211:
Question 36:
Mark (✓) against the correct answer
A ladder is placed in such a way that its foot is 15 m away from the wall and its top reaches a window 20 m above the ground. The length of the ladder is
(a) 35 m
(b) 25 m
(c) 18 m
(d) 17.5 m
Answer:
Page No 211:
Question 37:
Mark (✓) against the correct answer
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
(a) 13 m
(b) 14 m
(c) 15 m
(d) 12.8 m
Answer:
Page No 211:
Question 38:
Mark (✓) against the correct answer
∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm. Then, AB = ?
(a) 2.5 cm
(b) 5 cm
(c) 10 cm
(d)
Answer:
Page No 212:
Question 1:
In the given figure, AB || CD, ∠ABO = 60° and ∠CDO = 40°. Then, find ∠BOD.
Answer:
Page No 212:
Question 2:
In the given figure, CE || BA. If ∠BAC = 70° and ∠ECD = 50°, find ∠ACB.
Answer:
Page No 212:
Question 3:
In the given figure, two straight lines AB and CD intersect at a point O such that ∠AOC = 50°.
Find: (i) ∠BOD (ii) ∠BOC.
Answer:
Page No 212:
Question 4:
In the given figure, AOB is a straight line and OC is ray such that∠AOC = (3x + 20)° and ∠BOC = (2x − 10)°. Find the value of x and hence find (i) ∠AOC and ∠BOC.
Answer:
Page No 212:
Question 5:
In a ∆ABC, If ∠A = 65°, ∠B = 45°, find ∠C.
Figure
Answer:
Page No 212:
Question 6:
In the given figure, x : y = 2 : 3 and ∠ACD = 120°. Find the values of x,y and z.
Answer:
Page No 212:
Question 7:
Two legs of a right triangle are 8 cm and 15 cm long. Find the length of the hypotenuse of the triangle.
Answer:
Page No 212:
Question 8:
In the adjoining figure, ABC is a triangle in which AD is the bisector of ∠A. If AD ⊥ BC, show that ∆ABC is isosceles.
Answer:
Page No 212:
Question 9:
Construct a ∆ABC in which BC = 5.3 cm, ∠B = 60° and AB = 4.2 cm. Also, draw the perpendicular bisector of AC.
Answer:
Page No 212:
Question 10:
Mark (✓) against the correct answer
The supplement of 35° is
(a) 55°
(b) 65°
(c) 145°
(d) 165°
Answer:
Page No 212:
Question 11:
Mark (✓) against the correct answer
In the given figure, AOB is a straignt line, ∠AOC = 56° and ∠BOC = x°. The value of x is
(a) 34
(b) 44
(c) 144
(d) 124
Answer:
Page No 212:
Question 12:
Mark (✓) against the correct answer
In ∆ABC, side BC has been produced to D such that ∠ACD = 125° and ∠BAC = 60°. Then ∠ABC = ?
(a) 55°
(b) 60°
(c) 65°
(d) 70°
Answer:
Page No 213:
Question 13:
Mark (✓) against the correct answer
In a ∆ABC, If ∠B = 40° and ∠C = 35°, then ∠A = ?
(a) 50°
(b) 55°
(c) 105°
(d) 150°
Answer:
Page No 213:
Question 14:
Mark (✓) against the correct answer
In a ∆ABC, If 2∠A = 3∠B = 6∠C, then ∠B = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer:
Page No 213:
Question 15:
Mark (✓) against the correct answer
In a ∆ABC, If A − B = 33° and B − C = 18°, then ∠B = ?
(a) 35°
(b) 55°
(c) 45°
(d) 57°
Answer:
Page No 213:
Question 16:
Mark (✓) against the correct answer
∆ABC is an isosceles right triangle in which ∠A = 90° and BC = 6 cm. Then AB = ?
(a)
(b)
(c)
(d)
Answer:
Page No 213:
Question 17:
Fill in the blanks.
(i) The sum of the angles of a triangle is ...... .
(ii) The sum of any two sides of a triangle is always ...... than the third side.
(iii) In ∆ABC, if ∠A = 90°, then BC2 = (......) + (......).
(iv) In ∆ABC, AB = AC and AD ⊥ BC, then BD = ...... .
(v) In the given figure, side BC of ∆ABC is produced to D and CE || BA. If ∠BAC = 50°
then ∠ACE = ...... .
Answer:
(i) The sum of the angles of a triangle is 180°.
(ii) The sum of any two sides of a triangle is always greater than the third side.
(iii) In ∆ABC, if ∠A = 90°, then:
BC2 = (AB2) + (BC2)
(iv) In ∆ABC:
AB = AC
AD ⊥ BC
Then, BD = DC
(v) In the given figure, side BC of ∆ABC is produced to D and CE || BA.
If ∠BAC = 50°, then ∠ACE = 50°.
Page No 213:
Question 18:
Write 'T' for true and 'F' for false
(i) If two parallel lines are cut by a transversal, then the alternate interior angles are equal.
(ii) If two lines intersect each other, then the vertically opposite angles are equal.
(iii) Each acute angle of an isosceles right triangle measures 60°.
(iv) A right triangle cannot have an obtuse angle.
Answer:
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