SOLUTION: Angle L and Angle M are complementary angles. Angle N and Angle P ae complementary angles. If angle L = y-2, angle M - 2x + 3, angle N = 2x-y, and angle P = x-1, what is the value

Algebra ->  Angles -> SOLUTION: Angle L and Angle M are complementary angles. Angle N and Angle P ae complementary angles. If angle L = y-2, angle M - 2x + 3, angle N = 2x-y, and angle P = x-1, what is the value      Log On


   

Question 31879This question is from textbook
: Angle L and Angle M are complementary angles. Angle N and Angle P ae complementary angles. If angle L = y-2, angle M - 2x + 3, angle N = 2x-y, and angle P = x-1, what is the values of x, y, angle L,angle M,angle N and angle P?
I have worked on this for three days, called my grandfather and he too can not figure it out. I know that they suppose to equal 90 degrees I just cant figure out how to get there.
Help PLEASE This question is from textbook

Found 3 solutions by Cintchr, venugopalramana, Earlsdon:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
Ohhh ... I love this one ...
if angles are complementary ... when added they equal 90 deg.
and if you have two sets of them ... the equal 180 degrees
1. L+M=90
2. N+P=90
3. L+M+N+P=180
4. L=y-2
5. M=2x+3
6. N=2x-y
7. P=x-1
Plug equations 4, 5, 6, and 7 into equation 3
+L%2BM%2BN%2BP=180+
+1y+-+2+%2B+2x+%2B+3+%2B+2x+-+1y+%2B+1x+-+1+=+180+
To better combine like terms ... rearange the numbers
+2x+%2B+2x+%2B+1x+%2B+1y+-+1y+-+2+%2B+3+-+1+=+180+
combine like terms (y's and constants cancel out)
+5x+=+180+
Divide by 5
+x+=+36+
Plug this back into equations 5 and 7
+M=2x%2B3+ and +P=x-1+
+M=2%2836%29%2B3+ and +P=36-1+
+M=72%2B3+ and +P=35+
+M=75+
Take the M and P values and plug them back into equations 1 and 2
+L%2BM=90+ and +N%2BP=90+
+L%2B75=90+ and +N%2B35=90+
+L=15+ and +N=55+
Plug these values back into equations 4 and 6 and solve (don't forget the x)
+L=y-2+ and +N=2x-y+
+15=y-2+ and +55=2%2836%29-y+
+17=y+ and +55=72-y+
+17=y+ and +-17=-y+
+17=y+ and +17=y+
OKAY ..... Looking back through ...
x=36
y=17
L=15
M=75
N=55
P=35

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Angle L and Angle M are complementary angles.
SO.....L+M=90..................I
Angle N and Angle P ae complementary angles.
SO.....N+P=90...................II
If angle L = y-2,..........................III
OK
angle M - 2x + 3,
I HOPE YOU MEAN ...M=2X+3.............................IV
angle N = 2x-y,........................V
OK
and angle P = x-1,..............................V1
OK
SUBSTITUTE EQNS III AND IV IN EQN.I...WE GET
Y-2+2X+3=90
2X+Y=90-3+2=89.................................VII
SUBSTITUTING EQNS.V AND VI IN EQN.II WE GET....
2X-Y+X-1=90
3X-Y=90+1=91......................................VIII
ADD EQNS VII AND VIII
2X+Y+3X-Y=89+91=180
5X=180
X=180/5=36
SUBSTITUTING IN EQN.VII
2*36+Y=89
Y=89-72=17
HENCE X=36 AND Y =17
L=Y-2=17-2=15
M=2X+3=2*36+3=72+3=75
N=2X-Y=2*36-17=72-17=55
P=X-1=36-1=35.......
YOU CAN CHECK THAT L+M=15+75=90.....AND.....N+P=55+35=90....OK
what is the values of x, y, angle L,angle M,angle N and angle P?
I have worked on this for three days, called my grandfather and he too can not figure it out. I know that they suppose to equal 90 degrees I just cant figure out how to get there.
Help PLEASE

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
L = y-2
M = 2x+3
L+M = 90, so:
(y-2)+(2x+3) = 90 Solve for y
y = -2x+89
N = 2x-y
P = x-1
N+P = 90, so:
(2x-y)+(x-1) = 90 Solve for y
y = 3x-91
y = y So:
-2x+89 = 3x-91 Solve for x.
5x = 180
x = 36
y = 3(36)-91
y = 108-91
y = 17
L = y-2
L = 17-2
L = 15 degrees
M = 2x+3
M = 2(36)+3
M = 72+3
M = 75 degrees
L+M = 15+75 = 90 degrees: Complementary angles.
N = 2x-y
N = 2(36)-17
N = 72-17
N = 55 degrees
P = x-1
P = 36-1
P = 35 degrees
N+P = 55+35 = 90 degrees: Complementary angles.