From the figure shown where MN is parallel to PQ:
m<MSR = 100°
m<STQ = 80°
By carefully observing the figure shown:
<MSR is vertically opposite to <NST
Vertically opposite angles are equal
m<NST = (17x + 15)
<NST is alternative to <PTS
Alternative angles are equal
Therefore, m<NST = m<PTS
m<NST = 17x + 15
m<PTS = 19x + 5
17x + 15 = 19x + 5
19x - 17x = 15 - 5
2x = 10
x = 10/2
x = 5
m<NST = 17x + 15
m<NST = 17(5) + 15
m<NST = 100°
Since m<MSR = m<NST
m<MSR = 100°
m<PTS = 19x + 5
m<PTS = 19(5) + 5
m<PTS = 100°
m<PTS + m<STQ = 180° (Sum of angles on a straight line)
100 + m<STQ = 180
m<STQ = 180 - 100
m<STQ = 80°
From the figure shown where MN is parallel to PQ:
m<MSR = 100°
m<STQ = 80°
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