Question

Figure TUVS is a parallelogram.

Parallelogram T U V S is shown. Angle U is (4 x + 9) degrees and angle V is (6 x minus 29) degrees.

Which angles equal 91°?

angles T and V
angles S and U
angles U and V
angles S and T

Answer 1

In a parallelogram adjacent angles are supplementary: U + V = 180.

(4x + 9) + (6x − 29) = 180 → 10x − 20 = 180 → x = 20.

Then V = 6(20) − 29 = 91°, and the opposite angle T is equal to V. So angles T and V equal 91°.