Question

In the given figure, $ABCD$ is a cyclic quadrilateral. Find $x$ and $y$.

Answer 1

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

Here, $ABCD$ is a cyclic quadrilateral.

Then,

$\angle A+\angle C={180}^{\circ }$

$⟹$ $2x+{14}^o+4x+4^o={180}^{\circ }$

$⟹$$6x+{18}^o={180}^{\circ }$

$⟹$$6x={180}^{\circ }-{18}^o$

$⟹$$6x={162}^o$

$⟹$$x={27}^o$.

Also,

$\angle B+\angle D={180}^{\circ }$ (Sum of opposite angles of cyclic quadrilateral $={180}^{\circ }$)

$⟹$$5y+5^o+{50}^o={180}^o$

$⟹$$5y={180}^o-{55}^o$

$⟹$$5y={125}^o$

$⟹$$y={25}^o$.