Question

The angle measures of quadrilateral RSTU are shown.

Answer 1

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

• m∠R=m∠T;
• m∠S=m∠U;
• m∠R+m∠S=m∠S+m∠T=180°.

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

If x=35°, then

• m∠R=(2·35)°=70°;
• m∠S=(3·35-35)°=70°;
• m∠T=(35+35)°=70°;
• m∠U=360°-(6·35)°=150°.

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

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

Answer 2

Answer:

the answer is c

Step-by-step explanation:

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