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Question 52313This question is from textbook Geometry
: Angle L and Angle M are complementary angles. Angle N and Angle P are complementary angles. If angle L=y-2, angle M=2x+3, angle N=2x-y, and P=x-1. Find the values of x, y, angle L, angle M, angle N, and angle P.
This question is from textbook Geometry
Answer by hard(12)   (Show Source):
You can put this solution on YOUR website! There are several ways to solve this equation. Below is just one of them.
Since they're complementary angles, you know that Angle L + Angle M = 90.
So -
y-2+2x+3=90
[Group like terms]
y+2x+1=90
[Subtract 1 from both sides]
y+2x=89
[Subtract 2x from both sides]
y=89-2x
You now have one "extended" value for y.
You also know that Angle N + Angle P = 90, as well.
2x-y+x-1=90
[Group like terms]
3x-y-1=90
[Add 1 to both sides]
3x-y=91
[Subtract 3x from both sides]
-y=91-3x
[Multiply both sides by -1]
y=-91+3x
Now you have two "extended" values for y. Since y=y, you can now set-up another equation.
-91+3x=89-2x
[Add 91 to both sides]
3x=180-2x
[Add 2x to both sides]
5x=180
[Divide both sides by 5]
x=36
Now that you know the simplified value of x, you can find the simplified value of y, by substituting the value of x into either of the "extended" values of y (y=-91+3x, or y=89-2x).
y=89-2(36)
y=89-72
y=17
Now you have the simplified values of both x and y: x=36 and y=17. All you have to do now is substitute these values into your equations once more.
Angle L=(17)-2
L=15
Angle M=2(36)+3
M=72+3
M=75
Angle N=2(36)-(17)
N=72-17
N=55
Angle P=(36)-1
P=35
Now check your work just to make sure it's correct!
Angle L + Angle M = 90
15+75=90
90=90
Angle N +Angle P = 90
55+35=90
90=90
So, your answers are correct!
I hope this wasn't too confusing! Good luck!
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