Question

Figure TUVS is a parallelogram.

Which angles equal 91°?

A. angles T and V
B. angles S and U
C. angles U and V
D. angles S and T

Answer 1

4x + 9 +6x -29 = 180
10x -20 = 180
10x = 200
x = 20

m<U = m<S = 4(20) + 9 = 89

m<T = m<V = 6(20) - 29 = 91

answer
A. angles T and V

Answer 2

(A) T and V

Explanation:

It is given that TUVS is a parallelogram.

Now, ∠U+∠V=180°

⇒4x+9+6x-29=180°

⇒10x-20=180°

⇒10x=200°

⇒x=20°

Thus, ∠U=4x+9=4(20)+9=80+9=89° and ∠V=6x-29=6(20)-29=120-29=91°.

Now, ∠T=∠V and ∠U=∠S because opposite angles of parallelogram are equal.

Therefore, ∠T=∠V=91° and ∠U=∠S=89°, thus only angle T and V equals 91°.

Thus, option A is correct.