Question

In a trapezium ABCD, side AB is parallel to side DC. If $\angle A={72}^{\circ }$ and $\angle C={120}^{\circ }$, then values of $\angle B$ and $\angle D$ are -

• A. $\angle B={60}^{\circ }$ $\angle D={108}^{\circ }$
• B. $\angle B={108}^{\circ }$ $\angle D={60}^{\circ }$
• C. $\angle B={78}^{\circ }$ $\angle D={120}^{\circ }$
• D. $\angle B={60}^{\circ }$ $\angle D={120}^{\circ }$

Answer 1

The correct option is A

$\angle B={60}^{\circ }$

$\angle D={108}^{\circ }$

$\angle A={72}^{\circ }$ and $\angle C={120}^{\circ }$

$\angle A+\angle D={180}^{\circ }$ (Co-interior angles)

$\Rightarrow {72}^{\circ }+\angle D={180}^{\circ }$

$\Rightarrow \angle D={180}^{\circ }-{72}^{\circ }$

$\Rightarrow \angle D={108}^{\circ }$

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

$\Rightarrow \angle B+{120}^{\circ }={180}^{\circ }$

$\Rightarrow \angle B={180}^{\circ }-{120}^{\circ }$

$\Rightarrow \angle B={60}^{\circ }$