The difference of two complementary angles is 18. What is the measure if the two angles
Hint complementary angles sum to 90 degrees
36 degree , 54 degree
To find the measures of the two complementary angles, we need to set up an equation using the given information.
Let's call one angle x, and its complement (90 degrees minus x) y.
We know that the difference between the two angles is 18 degrees. So, we can express this as:
x - y = 18
Next, we know that the sum of two complementary angles is always 90 degrees. Therefore, we can express this relationship as:
x + y = 90
Now, we have a system of equations with two variables (x and y). We can solve this system using any method (substitution, elimination, or graphing).
Let's solve it using the method of substitution:
From the first equation, we can express x in terms of y:
x = y + 18
Substitute the value of x in the second equation:
(y + 18) + y = 90
Combine like terms:
2y + 18 = 90
Subtract 18 from both sides:
2y = 72
Divide both sides by 2:
y = 36
Now, substitute the value of y back into the first equation to find x:
x - 36 = 18
x = 18 + 36
x = 54
Therefore, the two angles are 54 degrees and 36 degrees.