Answer
x=108$^{\circ}$
y=44$^{\circ}$
z=47$^{\circ}$
Work Step by Step
The sum of the measures of the angles within a triangle is 180$^{\circ}$.
m$\angle$NMR+m$\angle$MNR+m$\angle$MRN=180
43+65+m$\angle$MRN=180
m$\angle$MRN=72$^{\circ}$
Angle MRN and x are supplementary.
m$\angle$MRN+x=180
72+x=180
x=108$^{\circ}$
x+y+m$\angle$P=180
108+y+28=180
y=44$^{\circ}$
Angle NRQ and x are vertical angles so they are congruent. Angle RNQ is complimentary to angle MNR.
m$\angle$MNR+m$\angle$RNQ=90
65+m$\angle$RNQ=90
m$\angle$RNQ=25$^{\circ}$
m$\angle$RNQ+m$\angle$NRQ+z=180
25+108+z=180
z=47$^{\circ}$
