In the given figure, $O$ is the centre of the circle. If $\angle AOB = 145°$, then find the value of $x$.

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Question

In the given figure, $O$ is the centre of the circle. If $\angle AOB = 145°$, then find the value of $x$.

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Accepted Answer

Step 1: Take a point $P$ on the circumference and join $AP$ and $BP$. $\angle APB = \frac{1}{2} 	imes 145° = 72.5°$
Step 2: $\angle APB + \angle ACB = 180°$ (opposite angles of cyclic quadrilateral)
Step 3: $\Rightarrow \angle ACB = 180° - 72.5° = 107.5°$, i.e., $x = 107.5°$

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