SOLUTION: This is the problem out of the book. "Angle L and Angle M are complementary angles. Angle N and Angle P are complementary angles. If the measure of angle L=y-2, the measure of angl

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Question 212339: This is the problem out of the book. "Angle L and Angle M are complementary angles. Angle N and Angle P are complementary angles. If the measure of angle L=y-2, the measure of angle M=2x+3, the measure of angle N=2x-y, and the measure of angle P=x-1, find the values of x, y, and the measures of angles L, M, N, and O." Please help me I don't even know where to start.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
This is the problem out of the book. "Angle L and Angle M are complementary angles.
Angle N and Angle P are complementary angles.
If the measure of angle L=y-2, the measure of angle M=2x+3, the measure of angle N=2x-y, and the measure of angle P=x-1,
find the values of x, y, and the measures of angles L, M, N, and O
:
You can do this. A lot of steps, but each one is pretty simple
:
"Angle L and Angle M are complementary angles. "; from these statements write:
L + M = 90
:
"Angle N and Angle P are complementary angles."
N + P = 90
:
"If the measure of angle L = y-2, the measure of angle M=2x+3,"
L + M = 90
Substitute for L and M, do some basic algebra and you have:
(y-2) + (2x+3) = 90
2x + y - 2 + 3 = 90
2x + y + 1 = 90
2x + y = 90 - 1
2x + y = 89
:
the measure of angle N=2x-y, and the measure of angle P=x-1,
N + P = 90
Substitute for N and P and do the same as above
(2x-y) + (x-1) = 90
2x + x - y - 1 = 90
3x - y = 90 + 1
3x - y = 91
:
We can use elimination with these two equations
3x - y = 91
2x + y = 89
--------------addition eliminates y, find x
5x = 180
x = 180%2F5
x = 36
:
Find y using the equation 2x + y = 89, substitute for x
2(36) + y = 89
72 + y = 89
y = 89 - 72
y = 17
;
We know the values: x=36; y=17
:
" find the measures of angles L, M, N, and O,
use the given equation and substitute for x and y
L = y - 2
L = 17 - 2
L = 15
:
M = 2(36) + 3
M = 72 + 3
M = 75
We can check this: 15 + 75 = 90 as L and M are complimentary
:
N = 2x - y
N = 2(36) - 17
N = 72 - 17
N = 55
:
P = 36 - 1
P = 35
Check this for complimentary 55 + 35 = 90
:
we have
x = 36
y = 17
L = 15
M = 75
N = 55
P = 35
:
How about this, did it make sense? Any questions? ankor@att.net