Question

Two angles are complementary. the measure of one angle is 6° more than one-half of the measure of the other. find the measure of each angle.

Answer 1

First, write an equation system based on the problem
We could write "two angels are complementary" as
⇒ a + b = 90° (1st equation)
We could write "the measure of one angle is 6° more than one-half of the measure of the other" as
⇒ a = 6° +
`(1)/(2)`b (2nd equation)

Second, solve the equation system by substituting a from the second equation to the first equation
a + b = 90°
6° +
`(1)/(2)`b + b = 90°
6° +
`(3)/(2)`b = 90°

`(3)/(2)`b = 84°
b = 84° ×
`(2)/(3)`
b = 56°

Substitute the measurement of b
a + b = 90°
a + 56° = 90°
a = 90° - 56°
a = 34°

The answer are 56° and 34°

Answer 2

Complementary angles total 90°
One angle is 6 + .5x, so both angles added together is

`x + (6 + 0.5 x) = 90 \\ 1.5x + 6 = 90 \\ 1.5x = 84 \\ x = 56 \\ 90 - 56 = 34`
First, we add one angle to the other, and set it to 90°. Then, we simplify the equation. Then, we subtract 6 from both sides. Then we divide both sides by 1.5
The first angle is 56°
The second angle is 90 - 56, which is 34°