Question

perimeter = 164. solve for x and y.

Explanation:

Step1: Find the value of \(x\)

In a parallelogram, consecutive angles are supplementary.
So, \(x + 81^{\circ}=180^{\circ}\)
\(x=180^{\circ}- 81^{\circ}\)
\(x = 99^{\circ}\)

Step2: Find the value of \(y\)

The perimeter formula of a parallelogram is \(P = 2(a + b)\). Here \(a=y\) and \(b=y + 12\) (since opposite sides of a parallelogram are equal).
Given \(P=164\), so \(164=2(y+(y + 12))\)
First, divide both sides by \(2\): \(82=y+(y + 12)\)
Simplify the right - hand side: \(82 = 2y+12\)
Subtract \(12\) from both sides: \(2y=82 - 12\)
\(2y=70\)
Divide both sides by \(2\): \(y = 35\)

Answer:

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