An angle is 24 degrees greater than the measure of its complement. What is the measure of the larger of the two angles?
a -24 = 60-a
2 a = 84
a = 42
90 - a = 48
x + (x+24) = 90
Solve for x, then x+24.
I used 60 instead of 90
To find the measure of the larger angle, we first need to understand what complementary angles are. Complementary angles are two angles that add up to 90 degrees.
Let's assume that the measure of the smaller angle (complement) is x degrees. According to the problem, the larger angle is 24 degrees greater than its complement. So, we can express the measure of the larger angle as (x + 24) degrees.
Since the two angles are complementary, their sum must be 90 degrees. We can now set up an equation to solve for x:
x + (x + 24) = 90
Combining like terms, we have:
2x + 24 = 90
Next, let's isolate x by subtracting 24 from both sides of the equation:
2x = 90 - 24
2x = 66
Finally, we solve for x by dividing both sides of the equation by 2:
x = 66 / 2
x = 33
So, the measure of the smaller angle (complement) is 33 degrees.
Now, we can find the measure of the larger angle by substituting x back into the expression we set up earlier:
x + 24 = 33 + 24 = 57
Therefore, the measure of the larger angle is 57 degrees.