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.

18°
36°
54°
58°

Answer 1

Angle: x
Complement: 90 - x

Answer 2

Sum of the complements:
x + 90 - x = 90

Answer 3

2x??

Answer 4

Difference of their measures: x - (90 - x)

Answer 5

90 exceeds x - (90 - x) by 72
That means:
90 - [x - (90 - x)] = 72

Answer 6

Solve for x.

Answer 7

....

Answer 8

i distribute the negitive?

Answer 9

If x is more than 45, then subtract x from 90

Answer 10

so it would be a

Answer 11

A

Answer 12

90 - [x - (90 - x)] = 72

90 - [x - 90 + x] = 72

90 - [2x - 90] = 72

90 - 2x + 90 = 72

-2x + 180 = 72

-2x = -108

x = 54

The measure of one of the angles is 54.
Since complementary angles add to 90, the other angle is 90 - x.
90 - 54 = 36
Since they ask fot eh measure of the smaller angle, the answer is 36.

Answer 13

thank you man that much simpler

Answer 14

^the last sentence above should read:
Since they ask for the measure of the smaller angle, the answer is 36.

Answer 15

You're welcome.