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? 19. compare and contrast a chord and a diameter of a circle.

Explanation:

18.

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, $4x + x=90^{\circ}$.

Step2: Solve the equation

Combining like - terms, we get $5x=90^{\circ}$. Then, dividing both sides by 5, $x=\frac{90^{\circ}}{5}=18^{\circ}$.

Step3: Find the measure of each angle

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

A chord is a line segment that connects two points on the circumference of a circle. A diameter is a special chord that passes through the center of the circle. So, all diameters are chords, but not all chords are diameters.

Answer:

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

19.