Question

if ( m angle qps = 86 ), ( m angle rpt = 92 ), and ( m angle rps = 44 ), what is ( m angle qpt )? enter your answer. ( m angle qpt = ) ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 86^\circ \) and \( m\angle RPS = 44^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPR=\angle QPS - \angle RPS \).
\[
m\angle QPR=m\angle QPS - m\angle RPS=86^\circ - 44^\circ = 42^\circ
\]

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 92^\circ \) and we just found \( m\angle QPR = 42^\circ \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT=\angle QPR+\angle RPT \).
\[
m\angle QPT=m\angle QPR + m\angle RPT=42^\circ+ 92^\circ=134^\circ
\]

Answer:

\( 134^\circ \)