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Area of a Sector of a Circle

In the given ...

Question

In the given figure, if m(arc APC) = 60 $°$ and $∠$ BAC = 80 $°$
Find (a) $∠$ ABC
(b) m(arc BQC)

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Solution

Let, O be the centre of circle.
Construction: Join OA, OB and OC.

We know that the angle subtended by the arc at the centre is twice the angle subtended at any part of the circle.

(i) $∠$ ABC = $\frac{1}{2} m (arc APC) = \frac{1}{2} \times 60 ° = 30 °$

(ii) m(arc BQC) = 2 $∠$ BAC = 160 $°$

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