Question

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Then,

• A. $\angle C>\angle D$
• B. $\angle C=\angle D$
• C. $\angle C<\angle D$
• D. $\angle C+\angle D={180}^{\circ }$

Answer 1

The correct option is B $\angle C=\angle D$

As, AB || CD
$\angle A=\angle D={180}^{\circ }$ ( Angles on the same side of the transversal)
Also, $\angle C=\angle B={180}^{\circ }$ ( Angles on the same side of the transversal)
$\angle A+\angle D=\angle C=\angle B$
However, $\angle A=\angle B$ [Using the result obtained in (i)]
$\therefore \angle C=\angle D$