The difference of two complementary angles is 18. What is the measure if the two angles
( hint complementary angles sum to 90 degrees
a + b = 90
a - b = 18
----------- add
2 a = 108
a = 54
b = 90 - 54 = 36
The ans is 37.5 and 52.5
Well, well, well! If the difference between two complementary angles is 18, then I hope you're ready for a mathematical circus act! Let's call the smaller angle "x" and the larger angle "y". Since they are complementary, we know that x + y = 90. And if we subtract the smaller angle from the larger angle, we get y - x = 18.
Now here comes the trick part! We can use the first equation to express "y" in terms of "x", so we have y = 90 - x. Now we can substitute this value of "y" into the second equation:
(90 - x) - x = 18
And if we simplify the equation, it becomes:
90 - 2x = 18
Phew, math can be quite a clown-show sometimes! Now we just solve for "x" by subtracting 90 from both sides:
-2x = 18 - 90
-2x = -72
And if we divide by -2, we get:
x = -72 / -2
Now, let's bring out the magic wand and turn that negative number positive:
x = 36
And since x is the smaller angle and the two angles add up to 90, the larger angle is:
y = 90 - 36
y = 54
So, the two complementary angles are 36 degrees and 54 degrees. Ta-da!
To find the measure of the two angles, we first need to understand what complementary angles are.
Complementary angles are two angles that add up to 90 degrees.
Let's assume one angle is x.
Since the difference between the two angles is 18, we can set up the equation:
x - (90 - x) = 18
Simplifying the equation, we get:
x - 90 + x = 18
Combining like terms, we have:
2x - 90 = 18
Adding 90 to both sides:
2x = 18 + 90
2x = 108
Dividing both sides by 2:
x = 108/2
x = 54
So, one angle is 54 degrees.
To find the other angle, we can subtract this from 90:
90 - 54 = 36
Therefore, the two angles are 54 degrees and 36 degrees.