Question

The measurement of Đ PQR is
P
a
R
0
280
360
(int) 160
(iv) 260​

Answer 1

Answer:

We know angle subtended at centre by an arc is double the angle subtendedby it at any other point.

Reflex angle ∠POR= 2∠PQR

= 2 × 100°

= 200°

Now, ∠POR = 360° – 200 = 160°

Also,

PO = OR [Radii of a circle]

∠OPR = ∠ORP [Opposite angles of isosceles triangle]

In ∆OPR, ∠POR = 160°

∴ ∠OPR = ∠ORP = 10°

Method 2:

Consider PR as a chord of the circle. Take any point S on the major arc of the circle

PQRS is a cyclic quadrilateral