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.
