Question

Angle F and angle G are complementary . The measure of angle F is three times the measure of angle G. What is the measure of each angle?

Answer 1

`g` = 22.5°

`f` = 67.5°

Explanation:

Let’s create a system of equations for
`f` and
`g`.

Complementary angles are two angles that add up to 90°, so
`f+g=90`

Also,
`f` is thrice of g:
`f=3g`

We can now substitute
`3g` in
`f+g=90` for
`f`.

`3g + g = 90\\\\4g = 90\\\\g=22.5`

Now, we can find
`f` by substituting
`g` into either equation.

`f + 22.5 = 90\\\\f = 90-22.5\\\\f = 67.5`

Hope this helped!