Question

Two angles are complementary. The sum of the measures of first angle and half the measure of the second angle is 65°. How do you find the measures of the angles?

Answer 1

The first angle measures `40^@` and the second angle measures `50^@`.

Explanation:

Two angles a re said to be complemetary angles when they add up to give an angle of `90^@`.

Let's assume that `angleX` is the first angle and `angleY` is the second angle. You know that

`X + Y = 90^@`

Moreover, you know that if you add the first angle to half of the second angle, you get an angle of `65^@`. This means that you can write

`X + 1/2 * Y = 65^@`

Use the first equation to find `X` as a function of `Y`

`X = 90 - Y`

Plug this into the second equation to find `Y`

`90-Y + 1/2 Y = 65`

`-1/2Y = 65 - 90`

`Y = 2 * 25 = color(green)(50^@)`

This means that angle `X` is

`X = 90 - (50) = color(green)(40^@)`