Question

In the figure above, $\overline{AB}\parallel \overline{CD},\overline{AE}$ bisects $\angle BAC$ and $\overline{CE}$ bisects $\angle ACD$. Find the measure of $\angle AEC$ if the measure of $\angle BAC$ is ${82}^{\circ }$.

• A. ${86}^{\circ }$
• B. ${88}^{\circ }$
• C. ${90}^{\circ }$
• D. ${92}^{\circ }$
• E. Cannot be determined from the given information

Answer 1

Answer: (C)

${90}^{\circ }$

Given, $\angle A={82}^0$

Hence, $\angle C={180}^0-{82}^0={98}^0$...(angles on the same side of the tansversal).

Therefore, $\angle EAC=\frac{\angle A}{2}={41}^0$

Similarly $\angle ECA=\frac{\angle C}{2}={49}^0$

Therefore, $\angle CEA={180}^0-(\angle EAC+\angle ECA)={180}^0-\left(90\right)={90}^0$.