Question

if ( m angle qps = 117 ), ( m angle rpt = 108 ), and ( m angle rps = 61 ), what is ( m angle qpt )? enter your answer. ( m angle qpt = ) ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 117^\circ \) and \( m\angle RPS = 61^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPS=\angle QPR + \angle RPS \).
\( m\angle QPR=m\angle QPS - m\angle RPS=117^\circ - 61^\circ = 56^\circ \)

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 108^\circ \) and we just found \( m\angle QPR = 56^\circ \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT=\angle QPR+\angle RPT \).
\( m\angle QPT=m\angle QPR + m\angle RPT = 56^\circ+108^\circ=164^\circ \)

Answer:

\( 164^\circ \)