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 sum of the measures of all interior angles in a quadrilateral is always equal to 360°.

If m∠R = (2x)°, m∠S = (3x – 35)° and m∠T = (x + 35)°, then the measure of the angle U is

m∠U=360°-(2x)°-(3x-35)°-(x+35)°=360°-(2x)°-(3x)°+35°-x°-35°=360°-(6x)°.

If quadrilateral RSTU is parallelogram, then

Check this conditions: 2x=x+35 ⇒ x=35°.

If x=35°, then

You get quadrilateral RSTU that cannot be parallelogram, because 70°+70°≠180°.

 strictly correct choice is D (also choice C is correct)

cosine

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x