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)