MATH SOLVE

6 months ago

Q:
# 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. <-------

Accepted Solution

A:

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

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