Question

Find the measure of \(∠P\) and \(∠S\) if \(\bar {SP} || \bar{RQ}\) in Figure. (If you find \(m∠R\), is there more than one method to find \(m∠P\) ?)

Answer 1

\(\Rightarrow\) \(∠ P + ∠ Q = 180°\) (Angles on the same side of transversal)
\(\Rightarrow\) \(∠ P + 130° = 180°\)
\(\Rightarrow\) \(∠ P = 50°\)
\(\Rightarrow\) \(∠ R + ∠ S = 180°\) (Angles on the same side of transversal)
\(\Rightarrow\) \(90° + ∠ R = 180°\)
\(\Rightarrow\) \(∠ S = 90°\)
Yes. There is one more method to find the measure of \(m∠ P\).
\(m∠ R\) and \(m∠ Q \) are given. 
After finding \(m∠ S\), the angle sum property of a quadrilateral can be applied to find \(m∠ P\).