## Chapter 2 - Parallel lines and transversals

**Practice set 2.1**

**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 □**

**Ans:** ∠w

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**(2) ∠q and □**

**Ans:** ∠x

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**(3) ∠r and □**

**Ans:** ∠y

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**(4) ∠s and □**

**Ans:** ∠z

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**Interior alternate angles.**

**(5) ∠s and □**

**Ans:** ∠x

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**(6) ∠w and □**

**Ans:** ∠r

**2. Observe the angles shown in the figure and write the following pair of angles.**

**(1) Interior alternate angles**

**Ans: **

**∠c and ∠e**

**∠b and ∠h**

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**(2) Corresponding angles**

**Ans: **

**∠a and ∠e**

**∠b and ∠f**

**∠c and ∠g**

**∠d and ∠h**

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**(3) Interior angles**

**Ans: **

**∠c and ∠h**

**∠b and ∠e**

**Practice set 2.2**

**Practice set 2.2**

**1. Choose the correct alternative.**

**1. Choose the correct alternative.**

**(1) In the adjoining figure, if line m || line n and line p is a transversal then find x.**

**(A) 135° ****(B) 90° ****(C) 45°****(D) 40°**

**Ans:** Option (C) : 45°

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**Solution:**

**line m || line n and line p is a transversal**

**m∠BFG + m∠FGD = 180° … [Interior angles]**

**∴ 3x + x = 180°**

**∴ 4x = 180°**

**∴ x = \(\large \frac {180}{4}\)**

**∴ x = 45°**

**(2) In the adjoining figure, if line a || line b and line l is a transversal then find x.**

**(A) 90° **

**(B) 60° **

**(C) 45° **

**(D) 30°**

**Ans:** Option (D) : 30°

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**Solution:**

**line a || line b and line l is a transversal.**

**m∠UVS ≅ m∠PUV … [Alternate angles]**

**∵ m∠PUV = 4x**

**∵ m∠UVS = 4x**

**m∠UVS + m∠WVS = 180° … [Angles in a linear pair]**

**∴ 4x + 2x = 180°**

**∴ 6x = 180°**

**∴ x = \(\large \frac {180}{6}\)**

**∴ x = 30°**

**2. In the adjoining 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.**

**Solution:**

**Consider ∠z as shown in figure.**

**line p || line q and line t is a transversal.**

**∴ m∠z = 40° …(i) [Corresponding angles]**

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**m∠x + m∠z = 180° … [Angles in a linear pair]**

**∴ m∠x + 40⁰ = 180° … [From(i)]**

**∴ m∠x = 180° – 40°**

**∴ m∠x = 140°**

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**Consider ∠w as shown in the figure.**

**m∠w + 70° = 180° … [Angles in a linear pair]**

**∴ m∠w = 180° – 70°**

**∴ m∠w = 110° …(ii)**

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**line p || line q and line s is a transversal.**

**m∠y ≅ m∠w … [Alternate angles]**

**∵ m∠w = 110° **

**∴ m∠y =110° … [From (ii)]**

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**Ans:** The value of m∠x is 140° and m∠y is 110°.

**3. In the adjoining 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.**

**Solution:**

**line p || line q and line l is a transversal**

**m∠a + 80° = 180° … [Interior angles]**

**∴ m∠a= 180° – 80°**

**∴ m∠a= 100°**

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**line l || line m and line p is a transversal**

**∴ m∠c = 80° …(i) [Exterior alternate angles]**

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**line p || line q and line m is a transversal.**

**m∠b ≅ m∠c … [Corresponding angles]**

**∵ m∠c = 80°**

**∴ m∠b = 80° … [From (i)]**

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**Ans:** The values are;

**m∠a = 100°**

**m∠b = 80°**

**m∠c = 80°**

**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.**

**Solution:**

**line a || line b and line l is a transversal.**

**∴ m∠x = 105° …(i) [Corresponding angles]**

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**m∠y = m∠x … [Vertically opposite angles]**

**∴ m∠y = 105° … [From (i)]**

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**m∠z + 105° = 180° … [Angles in a linear pair]**

**∴ m∠z = 180° – 105°**

**∴ m∠z = 75°**

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**Ans:** The values are;

**m∠x = 105°**

**m∠y = 105°**

**m∠z = 75°**

**5. In the adjoining figure, line p || line l || line q. Find ∠ x with the help of the measures given in the figure.**

**Solution:**

**line p || line l and line IJ is a transversal.**

**m∠IJN = m∠JIH … [Alternate angles]**

**∴ m∠IJN = 40° …(i)**

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**line l || line q and line MJ is a transversal.**

**m∠MJN = m∠JMK … [Alternate angles]**

**∴ m∠MJN = 30° …(ii)**

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**Now, **

**m∠x = m∠IJN + m∠MJN … [Angle addition property]**

**∴ m∠x = 40° + 30° … [From (i) and (ii)]**

**∴ m∠x = 70°**

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**Ans:** The measure of m∠x = 70°