Question

if m∠qps = 36, m∠rpt = 92, and m∠rps = 44, what is m∠qpt? enter your answer. m∠qpt = ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 106 \) and \( m\angle RPS = 44 \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPR=\angle QPS - \angle RPS \).
\( m\angle QPR=m\angle QPS - m\angle RPS=106 - 44 = 62 \)

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 92 \) and we just found \( m\angle QPR = 62 \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT=\angle QPR+\angle RPT \).
\( m\angle QPT=m\angle QPR + m\angle RPT=62 + 92=154 \)

Answer:

\( 154 \)