Degrees of a Circle

Circles: Fractions to Degrees and Back

A prerequisite for our Circles Unit

Multiple Choice

How many 1 degree turns are in a full circle?

• 500

• 1000

• 360

• 15

360°

We've learned that circles are divided into 360 equal pieces called degrees.

In this lesson, we're going to practice converting fractions of a circle to the equivalent degrees and back again!

Multiple Choice

What is the measure of the shaded part of the circle?

• 180 degrees

• 90 degrees

• 360 degrees

• 40 degrees

Multiple Choice

What is the measure of the shaded part of the circle?

• 180 degrees

• 90 degrees

• 360 degrees

• 270 degrees

Multiple Choice

How many degrees are in 1 part of a circle that is cut into 4 parts?

• 180

• 75

• 90

• 360

Great work!

Keep going!

Multiple Choice

If an angle is a right angle, how many 1-degree turns does the angle have?

• 360
• 1
• 90
• 75

Multiple Choice

How many degrees are in the shaded part of this circle?

• 72

• 360

• 90

• 45

Multiple Choice

How many degrees are in the shaded part of this circle?

• 72

• 360

• 90

• 45

Multiple Choice

The circle is split up by 8 congruent angles. Which statement is true about the circle?

• Each angle would turn through 8 1° angles

• Each angle measures 90 degrees

• Each angle forms 1/8 of the circle

• Each angle measures 360 degrees

Now, what about fractions that aren't so pretty?

Multiple Choice

In a circle, 300° is the same as:

• $$\frac{2}{3}$$  

• $$\frac{15}{30}$$  

• $$\frac{4}{5}$$  

• $$\frac{5}{6}$$  

Multiple Choice

In a circle, 253° is the same as:

• $$\frac{253}{360}$$  

• $$\frac{18}{26}$$  

• $$\frac{54}{87}$$  

• $$\frac{2}{3}$$  

Challenge Zone

Multiple Choice

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch. (Hint: Find the area of the whole circle. How much of the whole circle is 100°? Use that to get your final answer.)

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find how far she ran to the nearest degree.(Hint: Find the circumference of the whole circle. How much of the whole circumference is 230 feet? Use that to get your final answer.)

• 47

• 74

• 94

• 123