Question

in a circle, PQ is the diameter. R is a point on the circle such that PR=QR. Find the measure of angle PQR​

Answer 1

Angle PQR=45°

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Answer 2

Given:

PR=QR

PQ is the diameter

To find:

Angle PQR

Solution:

The required measure of angle PQR is 45°.

Since PQ forms the diameter of the given circle, any angle formed in the semicircle will be equal to 90°.

So, angle PRQ=90°

Now, in ΔPRQ, PR=QR.

The angles corresponding to PR and QR are of equal measure.

Angle RPQ=Angle PQR

Angle RPQ+angle PQR+angle PRQ=180°

2(Angle PQR)+90°=180°

2(Angle PQR)=90°

Angle PQR=45°

Therefore, the measure of angle PQR is 45°.