Question

In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to ______.

Options

• 40°

• 80°

• 120°

• 50°

Answer 1

In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to 40°.

Explanation:

Let ∠R = x

PQ = QR  ...(Given)

∴ ∠R = ∠P = x

Now, in ΔPOR

∠P + ∠Q + ∠R = 180°  ...(Angle sum property)

⇒ x + 100° + x = 180°

⇒ 2x = 180° – 100° = 80°

⇒ x = `80^circ/2` = 40°

Thus, ∠R = 40°