Lines & Angles
Exercise 5.2
Question 1: State the property that is used in each of the following statements?
- If a||b, then ∠1 = ∠5
- If ∠4 = ∠6, then a||b
- 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