Question

find m∠z and m∠w in parallelogram wxyz. y x 5p - 43° z w 4p - 83° m∠z = ° m∠w = °

Explanation:

Step1: Use property of parallelogram

In a parallelogram, adjacent - angles are supplementary, so \((5p - 43)+(4p - 83)=180\).

Step2: Simplify the equation

Combine like - terms: \(5p+4p-43 - 83 = 180\), which gives \(9p-126 = 180\).

Step3: Solve for \(p\)

Add 126 to both sides of the equation: \(9p=180 + 126\), so \(9p=306\). Then divide both sides by 9: \(p=\frac{306}{9}=34\).

Step4: Find \(m\angle Z\)

Substitute \(p = 34\) into the expression for \(m\angle Z\): \(m\angle Z=4p-83\). So \(m\angle Z=4\times34 - 83=136 - 83 = 53^{\circ}\).

Step5: Find \(m\angle W\)

Since \(\angle Z\) and \(\angle W\) are adjacent angles in a parallelogram and adjacent angles are supplementary, \(m\angle W=180 - m\angle Z\). So \(m\angle W=180 - 53=127^{\circ}\).

Answer:

\(m\angle Z = 53^{\circ}\), \(m\angle W = 127^{\circ}\)