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## 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.
Corresponding angles

(ii) If ∠4 = ∠6, then a ∥ b.
Alternate interior angles

(iii) If ∠4 + ∠5 = 180o, then a ∥ b.
Interior angles on the same side of transversal are supplementary

Question 2: In the adjoining figure, identify

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

(ii) The pairs of alternate interior angles.
∠2 and ∠8, ∠3 and ∠5

(iii) The pairs of interior angles on the same side of the transversal.
∠2 and ∠5, ∠3 and ∠8

(iv) The vertically opposite angles.
∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8

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

∠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)

Taking ∠y on line m.

∠y = 110o (corresponding angles)
= ∠x + ∠y = 180°
= ∠x + 110° = 180°
= ∠x = 180° - 110°
= ∠x = 70°

(ii)

∠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) ∠DEF

(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)

= 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)

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)

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)