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Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2
August 9, 2019 by Laxmi
Maharashtra State Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2
Question 1.
Choose the correct alternative.
i. In the given figure, if line m || line n and line p is a transversal, then find x.
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 1
(A) 135°
(B) 90°
(C) 45°
(D) 40°
Solution:
(C) 45°
Hint:
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 2
line m || line n and line p is a transversal.
∴ m∠BFG + m∠FGD = 180°
…[Interior angles]
∴ 3x + x = 180°
∴ 4x = 180°
∴ x = 1804
∴ x = 45°
ii. In the given figure, if line a || line b and line l is a transversal, then find x.
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 3
(A) 90°
(B) 60°
(C) 45°
(D) 30°
Solution:
(D) 30°
Hint:
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 4
line a || line b and line l is a transversal.
∴ m∠UVS = m∠PUV
…[Alternate angles]
= 4x
m∠UVS + m∠WVS = 180°
… [Angles in a linear pair]
∴ 4x + 2x = 180°
∴ 6x = 180°
∴ x = 1806
∴ x = 30°
Question 2.
In the given figure, line p || line q. Line t and line s are transversals. Find measure of ∠x and ∠y using the measures of angles given in the figure.
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 5
Solution:
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 6
i. Consider ∠z as shown in figure.
line p || line q and line t is a transversal.
∴ m∠z = 40° …(i) [Corresponding angles]
m∠x + m∠z = 180° …[Angles in a linear pair]
∴ m∠x + 40o = 180° …[From(i)]
∴ m∠x= 180° – 40°
∴ m∠x = 140°
ii. Consider ∠w as shown in the figure.
m∠w + 70° = 180° …[Angles in a linear pair]
∴ m∠w = 180° – 70°
∴ m∠w = 110° …(ii)
line p || line q and line s is a transversal.
∴ m∠y = m∠w …[Alternate angles]
∴ m∠y =110° …[From (ii)]
∴ m∠x = 140°, m∠y = 110°
Question 3.
In the given figure, line p || line q, line l || line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 7
Solution:
i. line p || line q and line l is a transversal.
∴ m∠a + 80° = 180° …[Interior angles]
∴ m∠a= 180° – 80°
∴ m∠a= 100°
ii. line l || line m and line p is a transversal.
∴ m∠c = 80° …(i) [Exterior alternate angles]
iii. line p || line q and line m is a transversal.
∴ m∠b = m∠c … [Corresponding angles]
m∠b = 80° …[From (i)]
∴ m∠a = 100°, m∠b = 80°, m∠c = 80°
Question 4.
In the given figure, line a || line b, line l is a transversal. Find the measures of ∠x, ∠y, ∠z using the given information.
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 8
Solution:
line a || line b and line l is a transversal.
∴ m∠x = 105° …(i) [Corresponding angles]
ii. m∠y = m∠x … [Vertically opposite angles]
∴ m∠y = 105° …[From (i)]
iii. m∠z + 105° = 180° …[Angles in a linear pair]
∴ m∠z = 180°- 105°
∴ m∠z = 75°
∴ m∠x = 105°, m∠y = 105°, m∠z = 75°
Question 5.
In the given figure, line p || line l || line q. Find ∠x with the help of the measures given in the figure.
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 9
Solution:
Maharashtra Board Class 8 Maths Solutions Chapter 2 Parallel Lines and Transversals Practice Set 2.2 10
line p || line l and line IJ is a transversal.
m∠IJN = m∠JIH … [Alternate angles]
∴ m∠IJN = 40° …(i)
line l || line q and line MJ is a transversal.
m∠MJN = m∠JMK … [Alternate angles]
∴ m∠MJN = 30° …(ii)
Now, m∠x = m∠IJN + m∠MJN
…[Angle addition property]
= 40° + 30° …[From (i) and (ii)]
∴ m∠x = 70°
I hope it's help you