in a parallelogram wxyz, wxy= 72 degrees, zwy= 80 degrees.Calculate a- wzyb- xwzc - wyz
Accepted Solution
A:
Answer:Part a) m∠WZY=72°Part b) m∠XWZ=108°Part c) m∠WYZ=28°Step-by-step explanation:we know thatIn a parallelogram opposite angles are congruent and consecutive angles are supplementarysee the attached figure to better understand the problemPart a) Find the measure of angle WZYwe know thatm∠WZY≅m∠WXY ----> by opposite angleswe have m∠WXY=72°thereforem∠WZY=72°Part b) Find the measure of angle XWZwe know thatm∠XWZ+m∠WXY=180° ----> by consecutive angleswe have m∠WXY=72°substitutem∠XWZ+72°=180°m∠XWZ=180°-72°m∠XWZ=108°Part c) Find the measure of angle WYZwe know thatThe sum of the interior angles of a triangle must be equal to 180 degreesIn the triangle WZYm∠ZWY+m∠WZY+m∠WYZ=180° we have m∠ZWY=80°m∠WZY=72°substitute80°+72°+m∠WYZ=180° 152°+m∠WYZ=180° m∠WYZ=180°-152°m∠WYZ=28°