Question

if ( m angle qps = 109 ), ( m angle rpt = 96 ), and ( m angle rps = 53 ), what is ( m angle qpt )? enter your answer. ( m angle qpt = ) ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 109^\circ \) and \( m\angle RPS = 53^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPS = \angle QPR + \angle RPS \).
\[
m\angle QPR = m\angle QPS - m\angle RPS = 109^\circ - 53^\circ = 56^\circ
\]

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 96^\circ \) and we just found \( m\angle QPR = 56^\circ \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT = \angle QPR + \angle RPT \).
\[
m\angle QPT = m\angle QPR + m\angle RPT = 56^\circ + 96^\circ = 152^\circ
\]

Answer:

\( 152 \)