Question

find the measure of \\( \angle rus \\).

Explanation:

Step1: Recall the property of a straight angle

A straight angle is \(180^{\circ}\). So, \(\angle PUT = 180^{\circ}\).

Step2: Set up the equation

We know that \(\angle PUT=\angle PUQ+\angle QUR+\angle RUS+\angle SUT\). Let \(\angle RUS = x\). Then \(180^{\circ}=39^{\circ}+23^{\circ}+x + 28^{\circ}\).

Step3: Simplify the right - hand side of the equation

First, add the known angles: \(39 + 23+28=(39 + 23)+28 = 62+28=90\). So the equation becomes \(180^{\circ}=90^{\circ}+x\).

Step4: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation: \(x=180^{\circ}-90^{\circ}\).

Answer:

\(90^{\circ}\)