Question

perimeter = 164. solve for x and y.

Explanation:

Step1: Find the value of \(x\)

In a parallelogram, consecutive angles are supplementary. So \(x + 81^{\circ}=180^{\circ}\), then \(x = 180^{\circ}-81^{\circ}\).

Step2: Calculate the value of \(x\)

\(x=99^{\circ}\)

Step3: Use the perimeter formula of a parallelogram

The perimeter \(P = 2(a + b)\) of a parallelogram. Here \(a=y\), \(b=y + 12\). So \(P=2(y+(y + 12))\). Given \(P = 164\), then \(2(y+(y + 12))=164\).
First, simplify the equation: \(2(2y+12)=164\), \(4y+24 = 164\).
Then, solve for \(y\): \(4y=164 - 24\), \(4y=140\), \(y=\frac{140}{4}=35\).

Answer:

\(x = 99^{\circ}\), \(y = 35\)