Rs Aggarwal 2018 for Class 7 Math Chapter 1 - Integers

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Rs Aggarwal 2018 Solutions for Class 7 Math Chapter 1 Integers are provided here with simple step-by-step explanations. These solutions for Integers are extremely popular among Class 7 students for Math Integers 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 1 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 177:

Question 1:

In the given figure, l || m and t is a transversal.
If ∠5 = 70°, find the measure of each of the angles
∠1, ∠3, ∠4 and ∠8.

Answer:

$Given : l ∥ m t is a transversal . ∠ 5 = 70 ° ∠ 5 = ∠ 3 = 70 ° (alternate interior angles) ∠ 5 + ∠ 8 = 180 ° (linear pair) or 70 ° + ∠ 8 = 180 ° ∠ 8 = 110 ° ∠ 1 = ∠ 3 = 70 ° (vertically opposite angles) ∠ 3 + ∠ 4 = 180 ° (linear pair) or ∠ 4 = 180 - ∠ 3 = 180 - 70 = 110 °$

Page No 178:

Question 2:

In the given figure, l || m and t is a transversal. If ∠1 and ∠2 are in the ratio 5 : 7, find the measure of each of the angles
∠1, ∠2, ∠3 and ∠8.

Answer:

$Given : l ∥ m t is a transversal . ∠ 1 : ∠ 2 = 5 : 7 Let the angles measure 5 x and 7 x . ∠ 1 + ∠ 2 = 180 ° (linear pair) ∴ 5 x + 7 x = 180 or 12 x = 180 or x = 15 ∴ ∠ 1 = 5 x = 5 (15) = 75 ° and ∠ 2 = 7 x = 7 (15) = 105 ° ∠ 2 + ∠ 3 = 180 ° (linear pair) ∠ 3 = 180 - 105 = 75 ° ∠ 3 + ∠ 6 = 180 (interior angles on the same side of t h e transversal are supplementary) ∠ 6 = 180 - ∠ 3 = 105 ° and ∠ 6 = ∠ 8 = 105 ° (vertically opposite angles) ∴ ∠ 1 = 75 ° ∠ 2 = 105 ° ∠ 3 = 75 ° ∠ 8 = 105 °$

Page No 178:

Question 3:

Two parallel lines l and m cut by a transversal t. If the interior angles of the same side of t be (2x − 8)° and (3x − 7)°, find the measure of each of these angles.

Answer:

$Given : l ∥ m t is a transversal . Let : ∠ 1 = (2 x - 8) ° ∠ 2 = (3 x - 7) ° We know that the consecutive interior angles are supplementary . ∴ ∠ 1 + ∠ 2 = 180 ° or (2 x - 8) + (3 x - 7) = 180 or 5 x - 15 = 180 or 5 x = 195 or x = 39 ∠ 1 = (2 x - 8) = (2 \times 39 - 8) = 70 ° ∠ 2 = (3 x - 7) = (3 \times 39 - 7) = 110 °$

Page No 178:

Question 4:

In the given figure, l || m. If s and t be transversals such that s is not parallel to t. find the values of x and y.

Answer:

From the given figure:

$∠ 1 = ∠ 3 = 50 ° (corresponding angles) and ∠ 1 + x ° = 180 ° (linear pair) or x ° = 180 ° - 50 ° = 130 ° or x = 130 ∠ 2 = ∠ 4 = 65 ° (corresponding angles) and ∠ 2 + y ° = 180 ° (linear pair) or y ° = 180 ° - 65 ° = 115 ° or y = 115$

Page No 178:

Question 5:

In the given figure, ∠B = 65° and ∠C = 45° in ∆ABC and DAE || BC. If ∠DAB = x° and ∠EAC = y°, find the values of x and y.

Answer:

$Given : ∠ B = 65 ° ∠ C = 45 ° DAE ∥ BC The given lines are parallel . ∴ x ° = ∠ B = 65 ° (alternate angles when AB is taken as the transversal) y ° = ∠ C = 45 ° (alternate angles when AC is taken as the transversal) ∴ x = 65 y = 45$

Page No 178:

Question 6:

In the adjoining figure, it is given that CE || BA, ∠BAC = 80° and ∠ECD = 35°.
Find (i) ∠ACE, (ii) ∠ACB, (iii) ∠ABC.

Answer:

$Given : CE ∥ BA ∠ BAC = 80 °, ∠ ECD = 35 ° (i) ∠ BAC = ∠ ACE = 80 ° (alternate angles with AC as a transversal) (ii) ∠ ACB + ∠ ACD = 180 ° (linear pair) or ∠ ACB + ∠ ACE + ∠ ECD = 180 ° or ∠ ACB + 80 ° + 35 ° = 180 ° or ∠ ACB = 65 ° (iii) In ∆ ABC : ∠ BAC + ∠ ACB + ∠ ABC = 180 ° (angle sum property) 80 ° + 65 ° + ∠ ABC = 180 ° ∠ ABC = 35 °$

Page No 178:

Question 7:

In the adjoining figure, it is being given that AO || CD, OB || CE and ∠AOB = 50°
Find the measure of ∠ECD.

Answer:

$Given : AO ∥ CD OB ∥ CE ∠ AOB = 50 ° ∠ AOD = ∠ CDB = 50 ° (when AO ∥ CD and OB is the transversal) ∠ ECD + ∠ CDB = 180 ° (consecutive interior angles are supplementary, DB ∥ CE and C D is t h e transversal) ∠ ECD = 180 ° - 50 ° = 130 °$

Page No 178:

Question 8:

In the adjoining figure, it is given that AB || CD, ∠AOB = 50° and ∠CDO = 40°.
Find the measure of ∠BOD.

Answer:

$Given : AB ∥ CD ∠ ABO = 50 ° ∠ CDO = 40 ° Construction : Through O, draw EOF ∥ AB . ∠ ABO = ∠ BOF = 50 ° (alternate angles, when AB ∥ EF and OB is a transversal) ∠ FOD = ∠ ODC = 40 ° (alternate angles, when CD ∥ EF and OD is a transversal) ∠ BOD = ∠ BOF + ∠ FOD ∠ BOD = 50 ° + 40 ° = 90 °$

Page No 178:

Question 9:

In the given figure, AB || CD and a transversal EF cuts them at G and H respectively.
If GL and HM are the bisectors of the alternate angles ∠AGH and ∠GHD respectively, prove that GL || HM.

Answer:

$Given : AB ∥ CD GL and HM are angle bisectors of ∠ AGH and ∠ GHD, respectively . ∠ AGH = ∠ GHD (alternate angles) or \frac{1}{2} ∠ AGH = \frac{1}{2} ∠ GHD or ∠ LGH = ∠ GHM (given) Therefore, GL ∥ HM as we know that if the angles of any pair of alternate interior angles are equal, then the lines are parallel .$

Page No 179:

Question 10:

In the given figure, AB || CD,
∠ABE = 120°, ∠ECD = 100° and ∠BEC = x°
Find the value of x.

Answer:

$Given : AB ∥ CD ∠ ABE = 120 ° ∠ ECD = 100 ° ∠ BEC = x ° Construction : FEG ∥ AB Now, \sin c e A B ∥ F E G and A B ∥ C D, F E G ∥ C D ∴ E F G ∥ A B ∥ C D ∠ ABE = ∠ BEG = 120 ° (alternate angles) or x ° + y ° = 120 ° . . . . (i) ∠ DCE = ∠ CEF = 100 ° (alternate angles) or x ° + z ° = 100 ° . . . . . (ii) Also, x ° + y ° + z ° = 180 ° (FEG is a s traight line) . . . (iii) Adding (i) and (ii) : 2 x ° + y ° + z ° = 220 ° or, x ° + 180 ° = 220 ° (substi tuting (iii)) x ° = 40 ° ∴ x = 40$

Page No 179:

Question 11:

In the given figure, ABCD is a quadrilateral in which AB || DC and AD || BC.
Prove that ∠ADC = ∠ABC.

Answer:

$Given : AB ∥ CD AD ∥ BC ∠ 1 + ∠ 2 = 180 ° (AB ∥ CD and AD is the transversal) . . . (i) ∠ 2 + ∠ 3 = 180 ° (AD ∥ BC and AB is the transversal) . . . (ii) From (i) and (ii) : ∠ 1 + ∠ 2 = 180 ° = ∠ 2 + ∠ 3 ∠ 1 = ∠ 3 ∠ ADC = ∠ ABC$

Page No 179:

Question 12:

In the given figure, l || m and p || q.
Find the measure of each of the angles ∠a, ∠b, ∠c and ∠d.

Answer:

$Given : l ∥ m p ∥ q ∠ 1 = 65 ° ∴ ∠ 1 = ∠ a = 65 ° (vertically opposite angles) ∠ a + ∠ d = 180 ° (consecutive interior angles on the same side of a transversal are supplementary) or ∠ d = 180 ° - 65 ° = 115 ° ∠ c + ∠ d = 180 ° (consecutive interior angles on the same side of a transversal are supplementary) or ∠ c = 180 ° - 115 ° = 65 ° ∠ c + ∠ b = 180 ° (consecutive interior angles on the same side of a transversal are supplementary) or ∠ b = 180 ° - 65 ° = 115 ° ∴ ∠ a = 65 ° ∠ b = 115 ° ∠ c = 65 ° ∠ d = 115 °$

Page No 179:

Question 13:

In the given figure, AB || DC and AD || BC, and AC is a diagonal. If ∠BAC = 35°, ∠CAD = 40°, ∠ACB = x° and ∠ACD = y°, find the value of x and y

Answer:

$Given : AB ∥ DC AD ∥ BC ∠ BAC = 35 ° ∠ CAD = 40 ° ∴ ∠ BAC = y = 35 ° (alternate angles when AB ∥ DC) ∠ CAD = x = 40 ° (alternate angles when AD ∥ BC) ∴ x = 40 y = 35$

Page No 179:

Question 14:

In the given figure, AB || CD and CA has been produced to E so that ∠BAE = 125°.
If ∠BAC = x°, ∠ABD = x°, ∠BDC = y° and ∠ACD = z°, find the values of x, y, z.

Answer:

$Given : AB ∥ CD ∠ BAE = 125 ° ∠ CAB + ∠ BAE = 180 ° or 125 ° + x ° = 180 ° or x = 55 x + z = 180 ° (c onsecutive interior angles on the same side of transversal are s upplementary) z = 180 - x = 180 - 55 = 125 y + x = 180 ° (c onsecutive interior angles on the same side of transversal are s upplementary) y = 180 - x = 180 - 55 = 125$

Page No 179:

Question 15:

In each of the given figures, two lines l and m are cut by a transevrsal t.
Find whether l || m.

Answer:

$(i) ∠ 1 + ∠ 2 = 180 (linear pair) or 130^{°} + ∠ 2 = 180 ° or ∠ 2 = 50 ° \neq 40 ° = ∠ 3 ∴ l ∦ m (ii) ∠ 2 + ∠ 3 = 180 ° (linear pair) 35 ° + ∠ 3 = 180 ° ∠ 3 = 145 ° = 145 ° = ∠ 1 ∴ l ∥ m (iii) ∠ 2 + ∠ 3 = 180 (linear pair) ∠ 3 = 180 ° - 125 ° = 55 ° ∠ 3 = 55 ° \neq 60 ° = ∠ 1 ∴ l ∦ m$

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