Question

if m∠qps = 117, m∠rpt = 103, and m∠rps = 66, what is m∠qpt? enter your answer. m∠qpt = ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 117^\circ \) and \( m\angle RPS = 66^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPR=\angle QPS - \angle RPS \).
\[
m\angle QPR=m\angle QPS - m\angle RPS=117^\circ - 66^\circ = 51^\circ
\]

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 103^\circ \) and we just found \( m\angle QPR = 51^\circ \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT=\angle QPR+\angle RPT \).
\[
m\angle QPT=m\angle QPR + m\angle RPT=51^\circ+ 103^\circ=154^\circ
\]

Answer:

\( 154^\circ \)