Question

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

Options

• (2 + b)° 

• (3 – b)°

• (108 – b)°

• (180 – b)°

Answer 1

In the following figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)°, then the measure of ∠2 in terms of b is (108 – b)°.

Explanation:

Since, PQ || RS and line 1 is a transversal.

∴ ∠2 = ∠6 = (3a – b)°  ...(i) [Corresponding angles]

∠1 + ∠2 = 180°   ...[Angles on a straight line PQ]

⇒ ∠2 = 180° – (2a + b)°  ...(ii) [∵ ∠1 = (2a + b)° (given)]

From (i) and (ii), we have

⇒ (3a – b)° = 180° – (2a + b)°

⇒ 3a – b = 180° – 2a – b

⇒ 3a – b + 2a + b = 180°

⇒ 5a = 180°

⇒ a = `180^circ/5` = 36°

∴ a = 36°

Now, ∠2 – (3a – b)°  ...[From (i)]

⇒ ∠2 = (3 × 36° – b)° = (108 – b)°