Question

10)
in the figure, \\(\overrightarrow{ed}\\) and \\(\overrightarrow{ea}\\) are opposite rays, and \\(\overrightarrow{eb}\\) bisects \\(\angle aec\\).
if \\(m\angle aec = 108^\circ\\) and \\(m\angle aeb = 6x^\circ\\), then what is the value of \\(x\\)?

ich two angles are supplementary?
*hint: find a linear pair

e circumference of the circle is

Explanation:

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal parts. So, if \(\overrightarrow{EB}\) bisects \(\angle AEC\), then \(m\angle AEB = m\angle BEC\), and \(m\angle AEC = m\angle AEB + m\angle BEC = 2m\angle AEB\).

Step2: Substitute known values

We know \(m\angle AEC = 108^\circ\) and \(m\angle AEB = 6x^\circ\). From the angle bisector property, \(108 = 2\times(6x)\).

Step3: Solve for \(x\)

Simplify the equation: \(108 = 12x\). Then, divide both sides by 12: \(x=\frac{108}{12}=9\).

Answer:

\(x = 9\)