Question

In the given figure, $\angle BAD={75}^o$, $\angle DCF=x^o$ and $\angle DEF=y^o$. Find the values of $x$ and $y$.

Answer 1

In a cyclic quadrilateral we know that the exterior angle is equal to the interior opposite angle

So we get

$\angle BAD=\angle DCF={75}^o$

It can be written as

$\angle DCF=x={75}^o$

We get $x={75}^o$

We know that the opposite angles of a cyclic quadrilateral is ${180}^o$

So we get

$\angle DCF+\angle DEF={180}^o$

By substituting the values

${75}^o+\angle DEF={180}^o$

On further calculation

$\angle DEF={180}^o-{75}^o$

By subtraction

$\angle DEF=y={105}^o$

Therefore, the value of $x$ and $y$ is ${75}^o$ and ${105}^o$.