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