Answer
Angle M = 128°
Angle N = 128°
Angle P = 52°
Angle Q = 52°
Step-by-step explanation
Since the lines MN and PQ are shown to be parallel to each other and lines MP and NQ are equal in length to each other, angle M and angle N are congruent, that is,
Angle M = Angle N
8x - 16° = 6x + 20°
8x - 6x = 20° + 16°
2x = 36°
Divide both sides by 2
(2x/2) = (36°/2)
x = 18°
Angle M = 8x - 16° = 8(18°) - 16° = 144° - 16° = 128°
Angle N = 6x + 20° = 6(18°) + 20° = 108° + 20° = 128°
Then, we can confirm that Angle M and Amgle P are same side interior angles, that is, they sum up to give 180°
Angle M + Angle P = 180°
128° + Angle P = 180°
Angle P = 180° - 128° = 52°
Angle N and Angle Q are same side interior angles too
Angle N + Angle Q = 180°
128° + Angle Q = 180°
Angle Q = 180° - 128° = 52°
Hope this Helps!!!