Question

w x y z (4x - 4)° (2x + 10)°

Explanation:

Step1: Set up equation

Assume ray $WY$ is the angle - bisector of $\angle XWZ$. Then $\angle XWY=\angle YWZ$. So, $4x - 4=2x + 10$.

Step2: Solve 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: $x = 7$.

Step3: Find $\angle XWY$

Substitute $x = 7$ into the expression for $\angle XWY$: $\angle XWY=4x - 4=4\times7-4=28 - 4=24^{\circ}$.

Step4: Find $\angle YWZ$

Substitute $x = 7$ into the expression for $\angle YWZ$: $\angle YWZ=2x + 10=2\times7+10=14 + 10=24^{\circ}$.

Answer:

$x = 7$
$\angle XWY=24$
$\angle YWZ=24$