## Chapter 5 Lines and Angles Exercise 5.2

**Question 1: State the property that is used in each of the following statements?**

**(i) If a ∥ b, then ∠1 = ∠5.Answer:** Corresponding angles

**(ii) If ∠4 = ∠6, then a ∥ b.**

Answer:Alternate interior angles

Answer:

**Interior angles on the same side of transversal are supplementary**

(iii) If ∠4 + ∠5 = 180o, then a ∥ b.

Answer:

(iii) If ∠4 + ∠5 = 180o, then a ∥ b.

Answer:

**Question 2: In the adjoining figure, identify**

**(i) The pairs of corresponding angles.Answer:** ∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7

**(ii) The pairs of alternate interior angles.**

Answer:∠2 and ∠8, ∠3 and ∠5

Answer:

**(iii) The pairs of interior angles on the same side of the transversal.**

Answer:∠2 and ∠5, ∠3 and ∠8

Answer:

**(iv) The vertically opposite angles.**

Answer:∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8

Answer:

**Question 3: In the adjoining figure, p ∥ q. Find the unknown angles.**

**Answer:**

∠d = ∠125° (corresponding angles)

= ∠e + 125° = 180° (Linear pair)

= ∠e = 180° - 125°

= ∠e = 55°

∠f = ∠e = 55° (vertically opposite angles)

∠b = ∠d = 125° (vertically opposite angles)

∠c = ∠f = 55° (corresponding angles)

∠a = ∠e = 55° (corresponding angles)**Question 4: Find the value of x in each of the following figures if l ∥ m.(i)**

**Answer:**

Taking ∠y on line m.

∠y = 110o (corresponding angles)

= ∠x + ∠y = 180°

= ∠x + 110° = 180°

= ∠x = 180° - 110°

= ∠x = 70°**(ii)**

**Answer:**

∠x = 100° (corresponding angles)**Question 5: In the given figure, the arms of two angles are parallel.**

**If ∠ABC = 70°, then find(i) ∠DGC(ii) ∠DEFAnswer: **

(i) Let AB ∥ DG.

∠DGC = ∠ABC (corresponding angles)

∠DGC = 70°

(ii) Let BC ∥ EF.

∠DEF = ∠DGC (corresponding angles)

∠DEF = 70°

**Question 6: In the given figures below, decide whether l is parallel to m.**

(i)

(i)

**Answer:**

= 126o + 44° (sum of 2 interior angle on same side of transversal is equal to 180°)

= 170° ≠ 180°

Therefore, line l is not parallel to line m.**(ii)**

**Answer:**Taking ∠x on line n.

= 75° + 75° (sum of 2 interior angles on same side of transversal is equal to 180°)

= 150° ≠ 180°

Therefore, line l is not parallel to line m.

**(iii)**

**Answer:**Taking ∠x on line l.

= 123o + ∠x (sum of interior angle on same side of transversal is equal to 180°)

= 123° + 57°

= 180°

Therefore, line l is parallel to line m.**(iv)**

**Answer:**Taking ∠x on line l.

= ∠x + 98o = 180° (the sum of adjacent angles is equal to 180o)

= ∠x = 180° - 98°

= ∠x = 82°

Let ∠x and 72° be the corresponding angles.

= 72° + 82° (sum of 2 interior angles on same side of transversal is equal to 180°)

Therefore, line l is not parallel to line m.

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