Question

In the following figure, AE and BC are equal and parallel and the three sides AB, CD and DE are equal to one another. If angle A is ${102}^{\circ }$. Find angles AEC and BCD.

• A. ${98}^{\circ }$ and ${122}^{\circ }$
• B. ${58}^{\circ }$ and ${152}^{\circ }$
• C. ${48}^{\circ }$ and ${132}^{\circ }$
• D. ${78}^{\circ }$ and ${162}^{\circ }$

Answer 1

The correct option is D ${78}^{\circ }$ and ${162}^{\circ }$

$\angle AEC={78}^0$ ...[supplementary angles]

If a line parallel to AB is drawn, then $\Delta$ ECD will be an equilateral triangle.

So, $\angle DCE={60}^0$ and $\angle BCE={102}^o$.

Hence, $\angle BCD={162}^o$