Question

if m∠ qps = 109, m∠ rpt = 96, and m∠ rps = 53, what is m∠ qpt? enter your answer. m∠ 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 \( \angle QPR=\angle QPS - \angle RPS \).
\[
m\angle QPR=m\angle QPS - m\angle RPS=109^\circ - 53^\circ = 56^\circ
\]

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:

\( 152^\circ \)