Math Challenge


Read the information and complete the activities. When you finish, print this page and place it in your folder.

A circle is measured in units called degrees. (Let's not go into why at this point.You can visit the sites I listed below if you want to explore more about angles.)

The entire circle is 360 degrees. Half a circle is 180 degrees, and one quarter (1/4) of a circle is 90 degrees.

1. How many sections do you see in the circle above?

2. Since the circle has a total of 360 degrees, how many degrees is each section?

An angle is the space between two lines, called "rays," that have the same endpoint.

The letter "B" represents the endpoint. That end point is called "vertex." The letters A and B represent the rays. The angle is the space between the two rays.

Angles are measured in degrees. The number of degrees tell you how wide open the angle is. Degrees are marked by a ° symbol.

When measuring angles, you go counterclockwise. Imagine a clock.


Start to measure where the 3 would be on a clock. That would be called a zero angle because there is nothing in it - just a single ray going directly to the right. As would you go up to 2, 1, and 12 on a clock, you would be opening the angle. When you reached 3 o'clock again, you would have a complete rotation of 360 degrees.

3. Look at the letter L. If you place that letter on the circle, how many degrees would that letter have?

A 360 degree angle is an angle that does a full circle. The "L" shaped angle forms what is called a right angle.

You can measure angles with a tool called "protractor." A protractor represents half of a circle, or 180 degrees. You can buy a protractor at just about any store that carries school items.


We use the symbol ° for degrees. A half circle of rotation is 180° and a quarter circle 90° and so on. Can you calculate the number of degrees in 1/3 of a rotation? Here is how to think about it. We know that ...

1 rotation = 360°
so if we divide each side of that equation by 3 we get that

1/3 rotation = 360°/3=120°.

4. Below you are given fractions (parts) of a rotation. Calculate the measure of the angle in degrees. Always try first and ask for help if you need it!

A full rotation is a full turn around the circle. Fill in the boxes below.

1 full rotation is 360°
1/2 rotation is 180°
1/3 rotation
2/3 rotation
1/4 rotation
3/4 rotation
1/6 rotation
5/6 rotation


Links to visit! Click on the links and find out more about angles and degrees! - Practice measuring degrees in the sky!

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