Question

The angle measures of quadrilateral RSTU are shown.

m∠R = (2x)°

m∠S = (3x – 35)°

m∠T = (x + 35)°

The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?

A. Yes, opposite angles R and T can be made equal to each other if x = 35.
B. Yes, consecutive angles R and S can be made equal to each other if x = 35.
C. No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.
D. No, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilateral.

The Correct Answer is C. <-------

Answer 1

THE ANSWER IS C No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.

Answer 2

If <R=<T
2x=x+35
x=35
<R=<T=2*35=70

<S=3x-35=3*35-35=2*35=70

but <R+<S+<T+<U=360
<U=360- (70+70+70)
<U=360-210
<U=150
Impossible to be a parallelogram
C is the answer