Question

if ( m angle qps = 96 ), ( m angle rpt = 94 ), and ( m angle rps = 57 ), what is ( m angle qpt )? enter your answer. ( m angle qpt = ) ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 96^\circ \) and \( m\angle RPS = 57^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPR=\angle QPS - \angle RPS \).
\[
m\angle QPR=m\angle QPS - m\angle RPS=96^\circ - 57^\circ = 39^\circ
\]

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 94^\circ \) and we just found \( m\angle QPR = 39^\circ \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT=\angle QPR+\angle RPT \).
\[
m\angle QPT=m\angle QPR + m\angle RPT=39^\circ+ 94^\circ=133^\circ
\]

Answer:

\( 133 \)