Question

if m∠qps = 117, m∠rpt = 85, and m∠rps = 73, what is m∠qpt? enter your answer. m∠qpt = ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 117^\circ \) and \( m\angle RPS = 73^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPR \) and \( \angle RPS \) make up \( \angle QPS \).
\[
m\angle QPR = m\angle QPS - m\angle RPS = 117^\circ - 73^\circ = 44^\circ
\]

Step2: Find \( m\angle QPT \)

We know that \( m\angle RPT = 85^\circ \) and we just found \( m\angle QPR = 44^\circ \). To find \( m\angle QPT \), we add \( m\angle QPR \) and \( m\angle RPT \) because \( \angle QPT \) is made up of \( \angle QPR \) and \( \angle RPT \).
\[
m\angle QPT = m\angle QPR + m\angle RPT = 44^\circ + 85^\circ = 129^\circ
\]

Answer:

\( 129^\circ \)