Question

In a trapezium ABCD, AB || CD. Find $\angle A$ and $\angle B$ if $\angle C={110}^{\circ }$ and $\angle D={125}^{\circ }$.

• A. $\angle A={80}^{\circ }$, $\angle B={45}^{\circ }$
• B. $\angle A={45}^{\circ }$, $\angle B={80}^{\circ }$
• C. $\angle A={70}^{\circ }$, $\angle B={55}^{\circ }$
• D. $\angle A={55}^{\circ }$, $\angle B={70}^{\circ }$

Answer 1

The correct option is D $\angle A={55}^{\circ }$, $\angle B={70}^{\circ }$

In a trapezium ABCD,
$\angle A+\angle D={180}^{\circ }$
$\angle A+{125}^{\circ }={180}^{\circ }$
$\angle A={55}^{\circ }$
Similarly,
$\angle B+\angle C={180}^{\circ }$
$\angle B+{110}^{\circ }={180}^{\circ }$
$\angle B={70}^{\circ }$