Question

In the figure, O is the centre of the circle and PR = QR. What is the measure of ∠PQR? (i) 60°(ii) 110°(iii) 75°(iv) 45°

Answer 1

I)60 degrees

Step-by-step explanation:

Construction of PQ forming an equilateral triangle

Each angle of a an equilateral triangle=60 degrees

Answer 2

Answer:

Option (iv)- 45°

Measure of ∠PQR is 45°

Step-by-step explanation:

Given, in a circle with center O, there is a PR=QR condition true.

This is only possible in the case of semi-circle, where two equal chords join and form perpendicular triangle.

According to the figure drawn, let us write the given statements:

PR=QR  and ∠PRQ = 90° (The angle made by chords in the semi circle are always 90° )

∠RPQ=∠PQR = x° (Angles opposite to the equal sides are equal)

In ΔPRQ,

 ∠RPQ+∠PRQ+∠PQR= 180°

                    x°+x°+90°=180°

                               2x°=90°

                                ∴ x°=45°

Therefore, the measure of ∠PQR=45°