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?

Question

asked Aug 15, 2021 73.0k views

1 Answer

Bridie · Answer 1 · 2021-08-20T20:53:08+0000

Answer:

= 22.5°

= 67.5°

Explanation:

Let’s create a system of equations for
and
.

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

Also,
is thrice of g:
f=3g

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

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

Now, we can find
by substituting
into either equation.

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

Hope this helped!