Question

look at this diagram: if rt and uw are parallel lines and m∠rsq = 48.8°, what is m∠tsq?

Explanation:

Step1: Identify the relationship between angles

Since \(RT\) and \(UW\) are parallel lines, and \(QS\) is a transversal. \(\angle R S Q\) and \(\angle T S Q\) are adjacent angles on a straight - line. The sum of adjacent angles on a straight - line is \(180^{\circ}\).

Step2: Calculate \(m\angle TSQ\)

We know that \(m\angle RSQ + m\angle TSQ=180^{\circ}\). Given \(m\angle RSQ = 48.8^{\circ}\). Then \(m\angle TSQ=180^{\circ}-m\angle RSQ\). Substitute \(m\angle RSQ = 48.8^{\circ}\) into the formula: \(m\angle TSQ=180 - 48.8\).

$$m\angle TSQ = 131.2^{\circ}$$

Answer:

\(131.2^{\circ}\)