Question

wy bisects ∠xwz. (4x - 4)° (2x + 10)°. #16: x = __. your answer. #17: m∠xwy = __.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{WY}$ bisects $\angle XWZ$, then $\angle XWY=\angle YWZ$. So, $4x - 4=2x + 10$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $4x-2x - 4=2x-2x + 10$, which simplifies to $2x-4 = 10$. Then add 4 to both sides: $2x-4 + 4=10 + 4$, getting $2x=14$. Divide both sides by 2: $x=\frac{14}{2}=7$.

Step3: Find the measure of $\angle XWY$

Substitute $x = 7$ into the expression for $\angle XWY$, which is $4x-4$. So, $m\angle XWY=4\times7-4=28 - 4=24^{\circ}$.

Answer:

#16: $x = 7$
#17: $m\angle XWY=24^{\circ}$