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?

Answer 1

Answer is C...
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Answer 2

Answer:

No, RSTU can not be a parallelogram.

Step-by-step explanation:

Given,

The angles measures of quadrilateral RSTU are,

m∠R = (2x)°

m∠S = (3x – 35)°

m∠T = (x + 35)°

Since, the sum of all interior angles of a quadrilateral is 360°.

⇒ m∠R +  m∠S +  m∠T +  m∠U = 360°

⇒ (2x)°  + (3x – 35)°  + (x + 35)° + m∠U = 360°

⇒ 6x + m∠U = 360°     ( By operating like terms )

⇒ m∠U = 360° - 6x      ( Subtracting 6x on both sides )

Now, we know that, the opposite angles of parallelogram are congruent or equal,

If RSTU is a parallelogram,

Then, m∠R =  m∠T and  m∠T = m∠U,

When, m∠R =  m∠T ⇒ (2x)° = (x + 35)° ⇒ x = 35°,

But, for x = 35°, 35+ 35 ≠ 360° - 6 × 35

⇒ m∠T ≠ m∠U

Hence, RSTU can not be a parallelogram.