Question

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

पर्याय

• 35°

• 45°

• 55°

• 70°

Answer 1

In the following 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)

Now, in ∆PRS,

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

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