# Lines & Angles

## Exercise 5.2

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

1. If a||b, then ∠1 = ∠5
2. If ∠4 = ∠6, then a||b
3. If ∠4 + ∠5 = 180°, then a||p

Answer: (a) Corresponding angles, (b) Alternate angles, (c) Sum of internal angles on one side of transversal

Question 2: In the adjoining figure, identify

(a) The pairs of corresponding angles

Answer: ∠4 and ∠8

∠1 and ∠5

(b) The pairs of alternate interior angles

Answer: ∠3 and ∠5

∠2 and ∠8

(c) The pair of interior angles on the same side of transversal

Answer: ∠3 and ∠8

∠2 and ∠5

(d) The vertically opposite angles

Answer: ∠4 and ∠ 2

∠ 1 and ∠ 3

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

Answer: ∠d = 125&° (Corresponding angles)

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

∠e + 125° = 180° (Linear pair of angles)

So, ∠e = 180° - 125° = 55°

∠ = ∠f = 55° (Vertically opposite angles)

∠a = ∠e = 55° (corresponding angles)

∠a = ∠c = 55° (vertically opposite angles)

Thus, ∠a = 55°, ∠b = 125°, ∠c = 55°, ∠ = 125°, ∠e = 55° and ∠f = 55°

Question 4: Find the value of x in each of the following figures, if l||m.

Answer: (i) Linear pair of 110° = 180° - 110° = 70°

∠x=70° (corresponding angles)

Answer: (ii) ∠x=100° (Corresponding angles)

Question 5: In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find

(a) ∠DGC

Answer: ∠DGC = ∠ABC = 70° (corresponding angles)

(b) ∠DEF

Answer: ∠DEF = ∠DGC = 70° (corresponding angles)

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

Answer: (i) No, (ii) No, (iii) Yes, (iv) No