Question

In the given figure, if PQ || RS and QR || TS, then the value a is ______.

Options

• 95°

• 90°

• 85°

• 75°

Answer 1

In the given figure, if PQ || RS and QR || TS, then the value a is 95°.

Explanation:

Since, PQ || RS and RQ is a transversal

∴ ∠PQR – ∠QRS = 85°  ......(i) [Alternate interior angles]

Also, RQ || TS and RS is a transversal.

∴ ∠QRS – ∠TSR = 85°   ......(ii) [Using (i)] [Alternate interior angles]

Now, RS is a straight line.

∴ ∠RST + a = 180°  ......[Linear pair]

⇒ 85° + a = 180°  ......[Using (ii)]

⇒ a = 180° – 85° = 95°