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Given: segment LM and segment QR are parallelgiven: m

Given: segment LM and segment QR are parallelgiven: m-example-1
User No Nein
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1 Answer

8 votes
8 votes

Answer

Angle QNP = 130°

Step-by-step explanation

Angle M = Angle L = 50°

We can then find Angle N in triangle MLN because the sum of angles in a triangle is 180°

Angle M + Angle L + Angle N = 180°

50° + 50° + Angle N = 180°

100° + Angle N = 180°

Angle N = 180° - 100° = 80°

Angle N = Angle LNM = 80°

Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.

So, since LM and QR are parallel to each other, we can easily see that

Angle MNR = Angle M = 50° (Alternate angles are equal to each other)

We can then find Angle RNP using the fact that the sum of angles on a straight line is 180°

Angle LNM + Angle MNR + Angle RNP = 180° (Sum of angles on straight line LNP)

80° + 50° + Angle RNP = 180°

130° + Angle RNP = 180°

Angle RNP = 180° - 130°

Angle RNP = 50°

We can then easily find Angle QNP.

Angle QNP + Angle RNP = 180° (Sum of angles on straight line RQ)

Angle QNP + 50° = 180°

Angle QNP = 180° - 50°

Angle QNP = 130°

Hope this Helps!!!

User Super Noob
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