Question

In the following figure, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is ______.

Options

• 55°

• 40°

• 50°

• 45°

Answer 1

In the following figure, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is 40°.

Explanation:

Here,

∠1 + ∠P = 180°  ...[Linear pair]

⇒ ∠1 + 140° = 180°

⇒ ∠1 = 180° – 140°

⇒ ∠1 = 40°

Since, PQ = PR

∴ ∠Q = ∠R = x  ...[Say]

In ΔPQR,

∠P + ∠Q + ∠R = 180°  ...[Angle sum property of a triangle]

⇒ 40° + x + x = 180°

⇒ 2x = 180° – 40°

⇒ 2x = 140°

⇒ x = 70°

So, ∠Q = ∠R = 70°

Given that, RS = RQ 

∴ ∠2 = ∠3 = 70°

In ΔSQR,

∠2 + ∠3 + ∠4 = 180°  ...[Angle sum property of a triangle]

⇒ 70° + 70° + ∠4 = 180°

⇒ ∠4 = 180° – 140°

⇒ ∠4 = 40°

Also, ST || QR  ...[Given]

Now, ∠4 = ∠6 = 40°  ...[Alternate interior angles]

∴ ∠TSR = 40°