Question

in the figure ,O is the centre of a circle and PR=QR . What is the measure of angle PQR​

Answer 1

Answer:

pqr is 45°

becoz a triangle ️ in semi circle will b right angled triangle

so as pr=qr

it implies angle rpq = angle pqr

Answer 2

Given:

O is the center of a circle.

PQ = QR

To Find:

measure of ∠PQR

Solution:

A triangle in a semi-circle will be a right-angled triangle,

In ΔPQR,

⇒ PR = QR [given]

Opposite angles of the equal sides are equal.

So, it implies that ∠RPQ = ∠PQR

∠QRP = 90° because the angle is inscribed in a semi-circle.

Then, by angle sum property of triangle is 180°

⇒ ∠PQR + ∠QRP + ∠RPQ = 180°

⇒ ∠RPQ + 90° + ∠RPQ =180°

⇒ 2∠RPQ = 180° - 90°

⇒ 2∠RPQ = 90° [divide 90/2]

⇒ ∠RPQ = 90/2

⇒ ∠RPQ = 45°

Therefore, the measure of ∠PQR = 45°.