Question

In the above trapezium ABCD, AB || CD. If $\angle A={50}^{\circ }$ and $\angle B={75}^{\circ }$, then find $\angle C$ and $\angle D.$

• A. $\angle C={130}^{\circ },\angle D={105}^{\circ }$
• B. $\angle C={105}^{\circ },\angle D={90}^{\circ }$
• C. $\angle C={90}^{\circ },\angle D={130}^{\circ }$
• D. $\angle C={105}^{\circ },\angle D={130}^{\circ }$

Answer 1

The correct option is D $\angle C={105}^{\circ },\angle D={130}^{\circ }$

$\text{Given:}\angle A={50}^{\circ }and\angle B={75}^{\circ }$
In a trapezium ABCD,

$\angle A+\angle D={180}^{\circ }...\left(i\right)$
$\text{[Co-interior angles are supplementary]}$
Similarly,
$\angle B+\angle C={180}^{\circ }...\left(ii\right)$

So, from (i)
${50}^{\circ }+\angle D={180}^{\circ }$
$\Rightarrow \angle D={130}^{\circ }$

Similarly, from (ii)
${75}^{\circ }+\angle C={180}^{\circ }$
$\Rightarrow \angle C={105}^{\circ }$