Question

<L and <M are complementary angles. <N and <P are complementary angles. If m<L = y-2, m<M = 2x+3, m<N = 2x-y, and m<P = x-1, find the values of x,y,m<L,m<M,m<N,and m<P.

how do you work this out?

Answer 1

If L and M add to 180, then
y-2+2x+3=180 simplify that, then use
N+P=180 or
2x-y+x-1=180 simplify that,

Now you have two standard equations. Solve for x and y.

Answer 2

Complementary angles add up to 90º
Bob must have been thinking of supplementary angles

take his two equations and set them equal to 90 instead of 180, that is ...
y-2+2x+3=90 and 2x-y+x-1=90

now solve for x and y, (I got x=36, y=17 ,L=15, M=75, N= 55, and P=35)