Question

Quadrilateral mntu below is a parallelogram. if m∠u = 5x and m∠t = 2x – 9, what is the measure of ∠t?

Answer 1

1. A property a parallelogram must have is that adjacent angles must be supplementary, they add up to 180º. We are given the values of the adjacent angles U and T. Their sum must add up to 180º. Solve for x. 
U + T = 180 
5x + 2x - 9 = 180 
7x - 9 = 180 
7x = 189 
x = 27 
Substitute this value of x for itself in angle T. 
T = 2(27) - 9 
T = 54 - 9 
T = 45, (D) is the answer