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

Answer:

$g$ = 22.5°

$f$ = 67.5°

Step-by-step 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!