Question

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ranger draws parallelogram rstu. if the interior angle measure of point s is 95 degrees, which statement must be true?
(1 point)
the interior angle measure of point u is 85 degrees
the interior angle measure of point r is 95 degrees
the measure of the interior angle at point t is 95 degrees
the interior angle measure of point u is 95 degrees
incorrect
adjacent angles in a parallelogram are supplementary

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram \(RSTU\), \(RS\parallel TU\) and \(RU\parallel ST\). Also, consecutive (adjacent) angles in a parallelogram are supplementary (\(\angle S+\angle T = 180^{\circ}\), \(\angle S+\angle R=180^{\circ}\)), and opposite angles are equal (\(\angle R=\angle T\), \(\angle S=\angle U\)).

Given \(\angle S = 95^{\circ}\).

Step2: Calculate adjacent and opposite angles

• For adjacent angles:

If \(\angle S = 95^{\circ}\), then \(\angle R=180^{\circ}-\angle S=180 - 95=85^{\circ}\), \(\angle T=180^{\circ}-\angle S = 85^{\circ}\)

• For opposite angles: \(\angle U=\angle S=95^{\circ}\)

Answer:

The interior angle measure of point \(U\) is \(95\) degrees.