Question

1. ∠f and ∠g are complementary. the measure of ∠f is four times the measure of ∠g. what is the measure of each angle?

Explanation:

Step1: Set up equations

Let the measure of $\angle G=x$. Then the measure of $\angle F = 4x$. Since $\angle F$ and $\angle G$ are complementary, $\angle F+\angle G = 90^{\circ}$. So $4x + x=90$.

Step2: Solve the equation

Combining like - terms, we get $5x=90$. Dividing both sides by 5, we have $x=\frac{90}{5}=18$.

Step3: Find the measure of each angle

The measure of $\angle G=x = 18^{\circ}$. The measure of $\angle F=4x=4\times18 = 72^{\circ}$.

Answer:

The measure of $\angle F$ is $72^{\circ}$ and the measure of $\angle G$ is $18^{\circ}$.