Question

17. In the given figure, O is the centre of circle.
+OPQ = 27c and +ORQ = 21c. The values of
+POR and +PQR respectively are
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Answer 1

Answer:

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Answer 2

Answer:∠POR =96 and ∠PQR=48

Step-by-step explanation:
Construction: Draw Line OQ such that OQ bisects ∠Q
OQ ,OP and OR are radii of the circle , ie , they are of the same length.
Consider Δ POQ and Δ ROQ
So,
ΔPOQ is an isosceles triangle , therefore

∠OPQ=27
∠OQP=27 (angles opposite to two equal sides  are equal in an isosceles triangle)
And
ΔROQ is an isosceles triangle , therefore

∠ORQ=21
∠OQR=21 (angles opposite to two equal sides  are equal in an isosceles triangle)
Therefore , ∠PQR=∠PQO+∠RQO
                              =27+21
                              =48

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Therefore , ∠POR = 2∠PQR
                               =2*48
                               =96
Therefore , ∠POR=96 and ∠PQR=48