# Lesson 5ERays and RadiansSolidify Understanding

### 1.

A circle has a radius of and a circumference of . How many times will the radius fit around the circumference?

### 2.

A circle has a radius of and a circumference of How many times will the radius fit around the circumference?

### 3.

If an angle measures , what is the measure of the angle in degrees?

### 4.

A semicircle has a radius of . The arc of the semicircle measures . How many times will the radius fit around the arc of the semicircle?

### 5.

A semicircle has a radius of . The arc of the semicircle measures . How many times will the radius fit around the arc of the semicircle?

### 6.

If an angle measures , what is the measure of the angle in degrees?

### 7.

If there are in a full circle, how many radians are there in a full circle?

### 8.

If an angle measures , what is the measure of the angle in degrees?

## Set

### 9.

Draw an angle of radian on circle .

Let be one side of the angle.

### 10.

If you laid the radius end to end around the circumference of , how many radii would it take to fit exactly?

### 11.

Label an angle of radians on circle .

### 12.

Find the ratio of as shown in the figure.

### 13.

One half of circle has been divided into equal parts. Label points , , and with the radian measures of angles , , and . Then write the corresponding degree measure for each angle.

### 14.

One half of circle has been divided into equal parts. Label points and with the radian measures of angles and . Then write the corresponding degree measure for each angle.

### 15.

What are the radian and degree measures of the angle of rotation from to in a counterclockwise direction?

Find the equivalent radian or degree measure of each angle based on what is given:

## Go

### 21.

• Locate the center of the circle.

• Draw a central angle and an inscribed angle that cuts the same arc as the central angle. What is the relationship between the measure of a central angle and its corresponding inscribed angle?

### 22.

• Locate the center of the circle.

• Draw a central angle and a circumscribed angle that cuts the same arc as the central angle. What is the relationship between the measure of a central angle and its corresponding circumscribed angle?