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Find the missing measures: Angle M, Angle N, Angle O, and Angle P.(8x - 16)(6x + 20)P

Find the missing measures: Angle M, Angle N, Angle O, and Angle P.(8x - 16)(6x + 20)P-example-1

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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!!!

User Simon Steele
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