Question

$ABCD$ is a trapezium in which $AB$ is parallel to $CD$. If $\angle A={36}^{\circ }$ and $\angle B={81}^{\circ }$, then find $\angle C$ and $\angle D$.

Answer 1

Given that, $ABCD$ is a trapezium with $AB\parallel CD,\angle A={36}^o$ and $\angle B={81}^o$.

To find out: The measure of $\angle C$ and $\angle D$.

We know that, if two parallel lines are intersected by a transversal line, the corresponding interior angles are supplementary.

$\therefore \angle A+\angle D={180}^o$

$\Rightarrow \angle D={180}^o-{36}^o$

$={144}^o$

Similarly,

$\angle B+\angle C={180}^o$

$\Rightarrow \angle C={180}^o-{81}^o$

$={99}^o$

Hence, $\angle C={99}^o$ and $\angle D={144}^o$.