**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.**