If $O$ is the centre of the circle, find the value of $x$ in each of the following figures:
"

Given:

$O$ is the centre of the circle.

To do:

We have to find the value of $x$.

Solution:

Let $CD$ meets $OB$ at $P$.

$\angle AOC = 135^o$

$\angle AOC + \angle COB = 180^o$                   (Linear pair)

$135^o + \angle COB = 180^o$

$\angle COB = 180^o- 135^o$

$= 45^o$

arc $BC$ subtends $\angle BOC$ at the centre and $\angle BPC$ at the remaining part of the circle

Therefore,

$\angle BOC = 2\angle BPC$

$\angle BPC = \frac{1}{2}\angle BOC$

$= \frac{1}{2} \times 45^o$

$= 22\frac{1}{2}^o$

The value of $x$ is $22\frac{1}{2}^o$.

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Updated on: 10-Oct-2022

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