Question

In a parallelogram wxyz, wxy= 72 degrees, zwy= 80 degrees.Calculate

Answer 1

Answer:

Part a) m∠WZY=72°

Part b) m∠XWZ=108°

Part c) m∠WYZ=28°

Step-by-step explanation:

we know that

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

see the attached figure to better understand the problem

Part a) Find the measure of angle WZY

we know that

m∠WZY≅m∠WXY ----> by opposite angles

we have

m∠WXY=72°

therefore

m∠WZY=72°

Part b) Find the measure of angle XWZ

we know that

m∠XWZ+m∠WXY=180° ----> by consecutive angles

we have

m∠WXY=72°

substitute

m∠XWZ+72°=180°

m∠XWZ=180°-72°

m∠XWZ=108°

Part c) Find the measure of angle WYZ

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

In the triangle WZY

m∠ZWY+m∠WZY+m∠WYZ=180°

we have

m∠ZWY=80°

m∠WZY=72°

substitute

80°+72°+m∠WYZ=180°

152°+m∠WYZ=180°

m∠WYZ=180°-152°

m∠WYZ=28°