Parallel Lines and Transversals
Maharashtra BoardClass8MathematicsChapter2
Solution
Practice Set 2.1
Question 1.
In the adjoining figure, each angle is shown by a letter. Fill in the boxes with the help of the figure.
Corresponding angles.
(1) ∠ p and [ ]
(2) ∠ q and [ ]
(3) ∠ r and [ ]
(4) ∠ s and [ ]
Interior alternate angles.
(5) ∠ s and [ ]
(6) ∠ w and [ ]
Corresponding angles.
(1) ∠ p and [ ∠ w ]
(2) ∠ q and [ ∠ x ]
(3) ∠ r and [ ∠ y ]
(4) ∠ s and [ ∠ z ]
Interior alternate angles.
(5) ∠ s and [ ∠ x ]
(6) ∠ w and [ ∠ r ]
Question 2.
Observe the angles shown in the figure and write the following pair of angles.
(1) Interior alternate angles
(2) Corresponding angles
(3) Interior angles
Interior alternate angles
(1) ∠ c and ∠ e (2) ∠ b and ∠ h
Corresponding angles
(1) ∠ a and ∠ e (2) ∠ d and ∠ h
(3) ∠ b and ∠ f (2) ∠ c and ∠ g
Interior angles
(1) ∠ b and ∠ e (2) ∠ c and ∠ h
Practice Set 2.2
Question 1.
Choose the correct alternative.
(a) In the adjoining figure, if line m ll line n and line p is a transversal then find x.
(A) 135° (B) 90° (C) 45° (D) 40°
∠ 3x + ∠ x = 180°
4x = 180 ∴ x= 45
Answer is (C) 45°
(b) In the adjoining figure, if line a ll line b and line l is a transversal then find x.
(A) 90° (B) 60° (C) 45° (D) 30°
∠ 4x + ∠ 2x = 180°
6x=180 ∴ x= 30
Answer is (D) 30°
Question 2.
In the adjoining figure line p ll line q. Line t and line s are transversals.
Find measure of Ð x and Ð y using the measures of angles given in the figure.
Consider ∠ a and ∠ b as shown in the ﬁgure. Line p ll line q and line t is the transversal.
m∠ a = 40° .... .. (Corresponding angles)
m∠ x + m∠ a = 180° …(Angles in linear pair)
∴ m∠ x + 40° = 180°
∴ m∠ x = 180°— 40°
∴ m∠ x = 140°
m∠ b = 70° (vertically opposite angles)
Line p ll q and line q is the transversal,
m∠ y + m∠ b = 180° ….(Interior angles)
∴ m∠ y + 70° = 180°
∴ m∠ y =180° — 70°
∴ m∠ y = 110°
Answer is m∠ x = 140°, m∠ y = 110°
Question 3.
In the adjoining figure. line p ll line q. line l ll line m. Find measures of ∠ a, ∠ b and ∠ c using the measures of given angles. Justify your answers.
Consider ∠ a as shown.
Line p  line q and line l is the transversal,
m∠ d=80° . . .. (Corresponding angles)
m∠ d + m∠ a = 180° … (Angles in a linear pair)
80 + m∠ a = 180°
m∠ a= 180°—80°
m∠ a= 100°
Line l  line m and line q is the transversal,
∠ b ≅ ∠ d …..(Exterior alternate angles)
m∠ b = m∠ d
∴ m∠ b = 80°
Line p  line q and line m is the transversal
∠ c ≅ ∠ b (Corresponding angles)
m∠ c = m∠ b
∴ m∠ c = 80°
Answer is m∠ a = 100°, m∠ b = 80° and m∠ c = 80°
Question 4.
In the adjoining figure, line a  line b. line l is a transversal. Find the measures of ∠ x, ∠ y, ∠ z using the given information.
Line a  line b and line l is the transversal,
m∠ x = 105° …..(Corresponding angles)
∠ y ≅ ∠ x ……(Vertically opposite angles)
m∠ y = m∠ x
∴ m∠ y = 105°
∴ m∠ z +105° = 180° (Angles in a linear pair)
∴ m∠ z =180°—105°
∴ m∠ z = 75°
Answer is m∠ x = 105°, m∠ y = 105° and m∠ z = 75°
Question 5.
In the adjoining figure, line p  line l  line q. Find ∠ x with the help of the measures given in the figure.
Consider ∠ m and ∠ n as shown :
Line p ll line l and on the transversal,
∠ m = 40° …….(Alternate angles)
Line l ll line q and on the transversal,
∠ n = 30° …….(Alternate angles)
∠ x = ∠ m+∠ n
∴ ∠ x = 40°+30° = 70°
Answer is m∠ x = 70°.
Extra Information :
If a transversal intersects two coplaner lines and a pair of

Practice Set 2.3
Question 1.
Draw a line l Take a point A outside the line. Through point A draw a line parallel to line l.
Question 2.
Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.
Question 3.
Draw a line m. Draw a line n which is parallel to line m at a distance of 4 cm from it.
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Notes : Chapter 2 : Parallel lines and transversals
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