Question

find $m\angle z$ in parallelogram $wxyz$.

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, $\angle X+\angle Y = 180^{\circ}$. Given $\angle X=a$ and $\angle Y = 3a - 100^{\circ}$, we have the equation $a+(3a - 100^{\circ})=180^{\circ}$.

Step2: Solve the equation for $a$

Simplify the left - hand side of the equation: $a + 3a-100^{\circ}=180^{\circ}$, which becomes $4a=180^{\circ}+ 100^{\circ}$. Then $4a = 280^{\circ}$, and $a = 70^{\circ}$.

Step3: Find $\angle Z$

In a parallelogram, $\angle Z=\angle X$ (opposite angles are equal). Since $a = 70^{\circ}$, $\angle Z=a = 70^{\circ}$.

Answer:

$70^{\circ}$