##
The measurement of Đ PQR is

P

a

R

0

280

360

(int) 160

(iv) 260

Question

The measurement of Đ PQR is

P

a

R

0

280

360

(int) 160

(iv) 260

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Mathematics
2 years
2021-07-08T04:03:12+00:00
2021-07-08T04:03:12+00:00 1 Answers
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## Answers ( )

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