Question

angles date: use the figure below to answer questions 1 - 4. 1. give another name for ∠2. 2. name the sides of ∠cbe. 3. in the figure, (overline{be}) bisects ∠cbd. if (mangle cbe=(3x - 7)^{circ}) and (mangle cbd = 94^{circ}), find the value of x.

Explanation:

Step1: Recall angle - bisector property

Since $\overline{BE}$ bisects $\angle CBD$, then $m\angle CBE=\frac{1}{2}m\angle CBD$.

Step2: Substitute given values

We know that $m\angle CBE=(3x - 7)^{\circ}$ and $m\angle CBD = 94^{\circ}$. So, $3x-7=\frac{1}{2}\times94$.

Step3: Simplify the right - hand side

$\frac{1}{2}\times94 = 47$, so the equation becomes $3x-7 = 47$.

Step4: Solve for $x$

Add 7 to both sides of the equation: $3x-7 + 7=47 + 7$, which gives $3x=54$. Then divide both sides by 3: $\frac{3x}{3}=\frac{54}{3}$, so $x = 18$.

Answer:

$x = 18$