Question 31879
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.