Quadrilateral RSTU is a parallelogram. If angle R measures $x$ degrees and angle S measures $70$ degrees, what must be the value of $x$?

• A. $90$
• B. $180$
• C. $70$
• D. $110$

Answer: (D)

Verified step by step guidance

1. Recall that in a parallelogram, opposite angles are equal, and adjacent angles are supplementary (their measures add up to 180 degrees).
2. Identify the given angles: angle S measures 70 degrees, and angle R measures x degrees.
3. Since angles R and S are adjacent angles in parallelogram RSTU, set up the equation for supplementary angles: \(x + 70 = 180\).
4. Solve the equation for \(x\) by subtracting 70 from both sides: \(x = 180 - 70\).
5. Conclude that the value of \(x\) is the difference found, which satisfies the properties of a parallelogram.