Question

1. construct viable arguments. \\( \angle rst \\) is adjacent to \\( \angle tsu, m \angle rst = 40 ^ { \circ } \\), and \\( m \angle tsu = 50 ^ { \circ } \\). explain how you can use the angle addition postulate to show that \\( \angle rsu \\) is a right angle.

Explanation:

Step1: Recall the Angle Addition Postulate

If two angles \( \angle RST\) and \( \angle TSU\) are adjacent, then \(m\angle RSU=m\angle RST + m\angle TSU\)

Step2: Substitute the given angle measures

We know that \(m\angle RST = 40^{\circ}\) and \(m\angle TSU=50^{\circ}\). Substituting these values into the Angle Addition Postulate formula:
\(m\angle RSU=40^{\circ}+ 50^{\circ}\)

Step3: Calculate the sum

\(m\angle RSU = 90^{\circ}\)

Answer:

Since \(m\angle RSU=90^{\circ}\), by the definition of a right - angle (\(a\) right - angle has a measure of \(90^{\circ}\)), \(\angle RSU\) is a right angle.