Question

In the given figure, PQ = PS. The value of x is ______.

विकल्प

• 35°

• 45°

• 55°

• 70°

Answer 1

In the given figure, PQ = PS. The value of x is 45°.

Explanation:

In ΔPQS, ∠2 + ∠3 = 110°  ......(i) [Exterior angle property of a triangle]

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

⇒ ∠4 = 180° = 110°  ......[Using (i)]

∴ ∠4 = 70°

Now, PQ = PS  ......(Given)

⇒ ∠2 = ∠4 = 70°  ......(ii)

(ii) Now, in ∆PRS,

∠2 = x + 25°  ......[Exterior angle property of a triangle]

⇒ x = 70° – 25° = 45°  ......[Using (ii)]