Question

$\angle B$ of an isosceles trapezium ABCD is ${82}^{\circ }$.

Find $\angle A,\angle Cand\angle D$.

• A. $\angle A={98}^{\circ },\angle C={98}^{\circ },\angle D={82}^{\circ }$
• B. $\angle A={82}^{\circ },\angle C={98}^{\circ },\angle D={82}^{\circ }$
• C. $\angle A={82}^{\circ },\angle C={98}^{\circ },\angle D={98}^{\circ }$
• D. $\angle A={82}^{\circ },\angle C={82}^{\circ },\angle D={98}^{\circ }$

Answer 1

The correct option is C

$\angle A={82}^{\circ },\angle C={98}^{\circ },\angle D={98}^{\circ }$

$Given:\angle B={82}^{\circ }$

$\Rightarrow \angle A=\angle B={82}^{\circ }\left(\text{Property of isosceles trapezium}\right)$

$\Rightarrow \angle C+\angle B={180}^{\circ }\left(\text{Co-interior angles}\right)$

$\Rightarrow \angle C+{82}^{\circ }={180}^{\circ }$

$\Rightarrow \angle C={180}^{\circ }-{82}^{\circ }={98}^{\circ }$

$Also\angle D=\angle C={98}^{\circ }\left(\text{Property of isosceles trapezium}\right)$

$\therefore \angle A={82}^{\circ },\angle C={98}^{\circ },\angle D={98}^{\circ }$