Answer:
Part a) m∠WZY=72°
Part b) m∠XWZ=108°
Part c) m∠WYZ=28°
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°