Question

In the adjoining figure, $ABCD$ is a trapezium in which $AB\parallel DC.$ If $\angle A={55}^{\circ }$ and $\angle B={70}^{\circ },$ find $\angle C$ and $\angle D.$

Answer 1

In a trapezium, the sum of the adjacent angles within the parallel lines is ${180}^{\circ }$.

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

$\angle D={180}^{\circ }-\angle A$

$={180}^{\circ }-{55}^{\circ }$

$={125}^{\circ }$

$\angle C={180}^{\circ }-{70}^{\circ }$

$={110}^{\circ }$

$\angle D={125}^{\circ }$ and $\angle C={110}^{\circ }$