Question

$\square ABCD$ is a trapezium in which $AB||DC$ and $\angle A=\angle B={45}^o$. Find $\angle C$ and $\angle D$ of the trapezium.

• A. ${135}^o$ each
• B. ${125}^o$, ${145}^o$
• C. ${145}^o$, ${125}^o$
• D. ${115}^o$, ${155}^o$

Answer 1

The correct option is A ${135}^o$ each

Given- $ABCD$ is a trapezium with $AB\parallel CD$, $\angle A=\angle B={45}^o$

To find out- $\angle D$ and $\angle C=?$

Solution-

$\angle A$ and $\angle D$ are the adjacent angles of the trapezium within $AB\parallel CD.$

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

$\Rightarrow {45}^O+\angle D={180}^O$

$\Rightarrow \angle D={135}^O$

Similarly $\angle B$ and $\angle C$ are the adjacent angles of the trapezium within $AB\parallel CD$.

$\therefore \angle B+\angle C={180}^O$

$\Rightarrow {45}^O+\angle C={180}^O$

$\angle C={135}^O$