Question

$overrightarrow{xy}$ bisects $\angle wxz$.

$x = ___$ $\angle yxz=___$ $\angle wxy=___$ $\angle wxz=___$

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{XY}$ bisects $\angle WXZ$, then $\angle WXY=\angle YXZ$. So, $7x - 7=5x + 3$.

Step2: Solve the equation for $x$

Subtract $5x$ from both sides: $7x-5x - 7=5x-5x + 3$, which simplifies to $2x-7 = 3$. Then add 7 to both sides: $2x-7 + 7=3 + 7$, getting $2x=10$. Divide both sides by 2: $x = 5$.

Step3: Find $\angle YXZ$

Substitute $x = 5$ into the expression for $\angle YXZ$. $\angle YXZ=5x + 3=5\times5+3=25 + 3=28^{\circ}$.

Step4: Find $\angle WXY$

Since $\angle WXY=\angle YXZ$, $\angle WXY = 28^{\circ}$.

Step5: Find $\angle WXZ$

$\angle WXZ=\angle WXY+\angle YXZ=28^{\circ}+28^{\circ}=56^{\circ}$.

Answer:

$x = 5$, $\angle YXZ=28^{\circ}$, $\angle WXY = 28^{\circ}$, $\angle WXZ=56^{\circ}$