Question

if m∠qps = 116, m∠rpt = 109, and m∠rps = 72, what is m∠qpt? enter your answer. m∠qpt = ?

Explanation:

Step1: Find \( m\angle QPR \)

We know that \( m\angle QPS = 116^\circ \) and \( m\angle RPS = 72^\circ \). To find \( m\angle QPR \), we subtract \( m\angle RPS \) from \( m\angle QPS \) because \( \angle QPR=\angle QPS - \angle RPS \).
\[
m\angle QPR=m\angle QPS - m\angle RPS=116^\circ - 72^\circ = 44^\circ
\]

Step2: Find \( m\angle SPT \)

We know that \( m\angle RPT = 109^\circ \) and \( m\angle RPS = 72^\circ \). To find \( m\angle SPT \), we subtract \( m\angle RPS \) from \( m\angle RPT \) because \( \angle SPT=\angle RPT - \angle RPS \).
\[
m\angle SPT=m\angle RPT - m\angle RPS = 109^\circ-72^\circ=37^\circ
\]

Step3: Find \( m\angle QPT \)

To find \( m\angle QPT \), we add \( m\angle QPR \), \( m\angle RPS \) and \( m\angle SPT \) (or we can also use \( m\angle QPS + m\angle SPT \) since \( \angle QPT=\angle QPS+\angle SPT \)).
\[
m\angle QPT=m\angle QPS + m\angle SPT=116^\circ+ 37^\circ = 153^\circ
\]
Or using the other way: \( m\angle QPT=m\angle QPR + m\angle RPS+m\angle SPT=44^\circ + 72^\circ+37^\circ=153^\circ \)

Answer:

\( 153 \)