Answer:
<NPM + <NZM = 146°
Step-by-step explanation:
Given:
In triangle STU: M, N and P are the midpoints of the line TU, US and ST respectively.
Line UZ is the altitude of the triangle STU
<TSU =71°, <TSU = 36°, <TUS = 73°
From the diagram:
N is the midpoint of line SU and M is the mid point of line UT.
∴ Line NM is parallel to line ST
P is the mid point of line ST and M is the mid point of line UT
∴Line PM is parallel to line SU
N is the mid point of line SU and P is the mid point of line ST
∴Line NP is parallel to line UT
Δ SPN = Δ STU = 36°
<SPN + <NPM + <MPT (Sum of angles in a triangle = 180°)
<UST = <MPT = 71°
36° + <NPM + 71° = 180°
<NPM + 107° = 180°
<NPM= 180°-107°
<NPM= 73°
In ΔSNZ, line SN = line NZ
∴ side SN = side NZ
< NSZ = <NZS = 71°
<MTZ = <MZT = 36°
<NZS + <NZM <MZT = 180° (Sum of angles in a triangle = 180°)
71° + <NZM + 36° = 180°
107° + <NZM = 180°
<NZM = 180° - 107°
<NZM = 73°
<NPM + <NZM =73° + 73°
<NPM + <NZM = 146°
