In the figure, $O$ is the centre of the circle and $\angle DAB = 50^o$. Calculate the values of $x$ and $y$.
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Given:

$O$ is the centre of the circle and $\angle DAB = 50^o$.

To do:

We have to find the values of $x$ and $y$.

Solution:

$ABCD$ is a cyclic quadrilateral.

This implies,

$\angle A + \angle C = 180^o$

$50^o + y = 180^o$

$y = 180^o - 50^o = 130^o$

In $\triangle OAB$,

$OA = OB$                 (Radii of the circle)

$\angle A = \angle OBA = 50^o$

$\angle DOB = \angle A + \angle OBA$

$x = 50^o + 50^o = 100^o$

Hence $x= 100^o$ and $y= 130^o$.

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Updated on: 10-Oct-2022

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