Question

In the figure above (not to scale) ABCD is trapezium in which $\overline{AB}\left|\right|\overline{CD}$ , AD = CD and AB = 2CD
If $\angle ADC={100}^{\circ }$ then find $\angle ABC$

• A. ${40}^{\circ }$
• B. ${50}^{\circ }$
• C. ${60}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is B ${50}^{\circ }$

Construction: Join $C$ and mid-point of $AB$

Now, $AECD$ is a rhombus

$\Rightarrow \angle ADC=\angle AEC={100}^o$

$\angle BEC={180}^o-{100}^o={80}^o$

And, $\angle EBC=\angle ECB$ (opposite sides are equal)

$\Rightarrow \angle EBC+\angle ECB+\angle BEC={180}^o$

$\Rightarrow \angle EBC={50}^o$