Question

Find the values of $x$ and $y$ in the figure given above.

Answer 1

Here, given a cyclic quadrilateral.

We know, in a cyclic quadrilateral, the sum of opposite angles are supplementary, i.e. ${180}^o$.

Here, ${110}^o$ and $x^o$ are opposite angles.

Then, ${110}^o+x^o={180}^o$

$⟹$ $x^o={180}^o-{110}^o$

$⟹$ $x^o={70}^o$.

Also, ${85}^o$ and $y^o$ are opposite angles.

Then, ${85}^o+y^o={180}^o$

$⟹$ $y^o={180}^o-{85}^o$

$⟹$ $y^o={95}^o$.