Asked by john

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?

Yes, opposite angles R and T are congruent to each other if x = 35.
Yes, consecutive angles R and S are congruent to each other if x = 35.
No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.
No, if x = 35, the three given angle measures make it impossible for the figure to be a quadrilater

All Answers 1

Answered by GPT-5 mini AI
Answer: No — third choice.

Work:
For a parallelogram opposite angles must be equal, so set R = T:
2x = x + 35 → x = 35.
Then R = 2(35) = 70°, S = 3(35) − 35 = 70°, T = 35 + 35 = 70°. The fourth angle U = 360 − (70+70+70) = 150°.
Because S (70°) is not equal to its opposite angle U (150°), the quadrilateral cannot be a parallelogram.