<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?
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.
Complementary angles add up to 90ยบ
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)
To find the values of x, y, m<L, m<M, m<N, and m<P, we will use the fact that complementary angles add up to 90 degrees.
Given conditions:
m<L = y - 2
m<M = 2x + 3
m<N = 2x - y
m<P = x - 1
Since <L and <M are complementary, we can write the equation:
m<L + m<M = 90
Substituting the given values:
(y - 2) + (2x + 3) = 90
Simplifying the equation:
y + 2x + 1 = 90
Since <N and <P are complementary, we can write another equation:
m<N + m<P = 90
Substituting the given values:
(2x - y) + (x - 1) = 90
Simplifying the equation:
3x - y - 1 = 90
Now, we have a system of two equations with two variables:
y + 2x + 1 = 90 ...(1)
3x - y - 1 = 90 ...(2)
Solving these equations simultaneously will give us the values of x and y.
To solve the system of equations, we can use the method of substitution or elimination:
Method 1: Substitution
From equation (1), we can isolate y:
y = 90 - 2x - 1
Substituting this value of y in equation (2):
3x - (90 - 2x - 1) - 1 = 90
Simplifying the equation:
3x - 90 + 2x + 1 - 1 = 90
5x - 90 = 90
Adding 90 to both sides:
5x = 180
Dividing both sides by 5:
x = 36
Substituting the value of x in equation (1):
y + 2(36) + 1 = 90
y + 72 + 1 = 90
y + 73 = 90
Subtracting 73 from both sides:
y = 17
So, x = 36 and y = 17.
Now, we can substitute these values of x and y back into the given equations to find the values of m<L, m<M, m<N, and m<P:
m<L = y - 2 = 17 - 2 = 15
m<M = 2x + 3 = 2(36) + 3 = 75
m<N = 2x - y = 2(36) - 17 = 55
m<P = x - 1 = 36 - 1 = 35
Therefore, the values are:
x = 36
y = 17
m<L = 15
m<M = 75
m<N = 55
m<P = 35