In Fig. 5.28, PQ || RS. If ∠ 1 = (2a + b)° and ∠ 6 = (3a–b)°, then the measure of ∠ 2 in terms of b is

Question

Philoid · Accepted Answer

∠1 = (2a + b)° …Equation (i)

∠6 = (3a–b)°

Since ∠5 and ∠6 forms a linear pair so

∠5 = (180-3a + b)°

∠5 = ∠1 = (180-3a + b)° (Corresponding angles) …Equation (ii)

Equating Equation (i) and Equation (ii) we get

2a + b = 180-3a + b

⇒ 5a = 180

⇒ a = 36⁰

Since ∠1 and ∠2 forms a linear pair so

∠2 = 180⁰- 2a-b

⇒ ∠2 = (108-b)⁰

In Fig. 5.28, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a–b)°, then the measure of ∠2 in terms of b is