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Question 485680: Problem:
Angle M and angle L are complementary angles. Angle N and angle P are complementary angles. If angle L equals y-2, angle M equals 2x+3, and angle N equals 2x-y, and angle P equals x-1. Find the values of x, y, angle L, angle M, angle N, and angle P.
I tried making an shape using two intersecting lines and labeling them L, M, N, and P, then putting the equation next to each one. Then I tried setting angle P and M equal to eachother since they are congruent angles. But I am just not sure you are supposed to do it that way.
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! I solved this using simultaneous equations.
2x + 3 + y - 2 = 90
2x -y + x -1 = 90
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2x + y + 1 = 90
3x - y - 1 = 90
__________________
2x + y = 89
3x - y = 91 (add the equations)
5x = 180
x = 36 degrees.
plugging into the first equation
72 + y + 3 -2 = 90
y = 17 degrees.
So,
Angle L = 17 - 2 = 15 degrees
Angle M = 2(36) + 3 = 75 degrees
Angles L + M = 90 degrees.
Angle N = 2(36) - 17= 55 degrees.
Angle P = 36 - 1 = 35 degrees.
Angles N + P = 90 degrees.
Cleomenius.
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