E and F are complementary. The measure of E is 54 degrees more than the measure of F. Find the measure of each angle.
18,72
To find the measure of each angle, we need to set up and solve a system of equations.
Let's represent the measure of angle E as x degrees, and the measure of angle F as y degrees.
Given that E and F are complementary, we know that their sum is equal to 90 degrees:
x + y = 90 ...(Equation 1)
We are also given that the measure of E is 54 degrees more than the measure of F:
x = y + 54 ...(Equation 2)
We can solve this system of equations by substitution or elimination. Let's use substitution:
From Equation 2, we can express x in terms of y:
y + 54 + y = 90
2y + 54 = 90
2y = 90 - 54
2y = 36
y = 18
Substitute the value of y back into Equation 1 to find the value of x:
x + 18 = 90
x = 90 - 18
x = 72
Therefore, the measure of angle E is 72 degrees, and the measure of angle F is 18 degrees.