Question

in the figure, $overrightarrow{ed}$ and $overrightarrow{ea}$ are opposite rays, and $overrightarrow{eb}$ bisects $angle aec$. if $mangle ced = 54^{circ}$ and $mangle aeb=(8x - 1)^{circ}$, then what is $mangle bec$? $mangle bec=square^{circ}$

Explanation:

Step1: Find the measure of ∠AEC

Since $\overrightarrow{ED}$ and $\overrightarrow{EA}$ are opposite rays, $\angle AED = 180^{\circ}$. Given $\angle CED=54^{\circ}$, then $\angle AEC=\angle AED - \angle CED$. So, $\angle AEC = 180^{\circ}-54^{\circ}=126^{\circ}$.

Step2: Use the angle - bisector property

Since $\overrightarrow{EB}$ bisects $\angle AEC$, then $\angle AEB=\angle BEC$. Also, we know that $\angle AEB=(8x - 1)^{\circ}$ and $\angle AEB=\frac{1}{2}\angle AEC$. Since $\angle AEC = 126^{\circ}$, then $\angle AEB=\angle BEC=\frac{126^{\circ}}{2}=63^{\circ}$.

Answer:

$63$