Question

The sum of the measures of two complementary angles exceeds the difference of their measures by 72°. Find the measure of the smaller angle.

A. 18°
B. 36°
C. 54°
D. 58°

Answer 1

If two angles are complementary it means they both add up to 90 degrees.

Sum - Difference = 72

90 - Difference = 72

90 - 72 = Difference.

18 = Difference.

Difference = 18.

Let the two angles be x and y.

x + y = 90
-
x - y = 18
__________
0 + 2y = 72
__________

2y = 72

y = 72/2

y = 36

The smaller angle is 36°

Option B.

Answer 2

we can write the question as an equation by doing this:
x + y = x - y + 72
Then, we can simplify the equation.
Add y to both sides:
x + 2y = x + 72
Subtract x from both sides:
2y = 72
Divide both sides by 2:
y = 36

Complementary angles add up to 90, and x and y are complementary. Since y is less than half of 90 (36 < 45), it must be the answer.

So, the answer is 36 degrees, or answer 'B'

Hope I helped and let me know if you have any questions :)