A girl with a skateboard and a robot dog at a skate ramp

What Is a Degree?

Maya's robot dog can spin and turn. But how do we measure a turn? Let's find out!

4th Grade Math

Step 1: The Full Circle

0

90

180

270

360

Maya's robot dog spins all the way around. A full circle is cut into tiny, equal turns. Each tiny turn is a degree. Look at the end of the scale. How many one-degree turns make a full circle?

A full circle holds 360 one-degree angles. The scale ends at 360, so a full spin measures 360 degrees.

Step 2: Count the One-Degree Angles

Each block stands for one one-degree turn. The robot dog turns through all of these tiny angles. Count them to determine the angle measure. What is the measure of this angle?

There are 12 blocks, so that is 12 one-degree angles. Turning through 12 one-degree angles measures 12 degrees.

Let's Remember

The Degree Rule

          A full circle = 360 one-degree angles.

          An angle that turns through n one-degree angles measures n degrees.

          Turn through 12? That is 12 degrees. Turn through 75? That is 75 degrees.

Maya says: Degrees are like tiny steps around a circle. Count the steps, and you know the angle!

Read the Degree Scale

0

15

30

45

60

75

90

This scale counts one-degree angles, marked every 15. An angle opens from 0 and turns through one-degree angles until it reaches 60. What is its measure?

The angle turned through 60 one-degree angles, from 0 all the way to 60. So it measures 60 degrees.

Watch Out!

A Common Mistake

          Some kids think longer sides make a bigger angle. That is wrong!

          Degrees count the turn, not the length of the sides.

          A 30-degree angle with long rays is still 30 degrees.

Analyze the turn, not the rays. Ask: how many one-degree angles did it pass through?

Solve It!

An angle turns through 72 one-degree angles.

Measure = ? degrees

Turning through 72 one-degree angles means the measure is exactly 72 degrees. The number of tiny turns IS the measure.

Word Problem

Maya opens a door slowly. The door swings through 35 one-degree angles before it stops. How many degrees did the door open?

The door turned through 35 one-degree angles, so it opened 35 degrees. Count the tiny turns to find the measure.

What Goes in the Blank?

A right angle makes perpendicular rays and measures 90 degrees.

90 degrees = ? one-degree angles

90 degrees means the angle turned through 90 one-degree angles. The rule works both ways!

Half a Circle

The robot dog makes a half turn. A full circle is 360 one-degree angles. How many degrees is a half turn?

Half of 360 is 360 ÷ 2 = 180. A half turn passes through 180 one-degree angles, so it measures 180 degrees.

The Clock Turn

A clock hand moves from the 12 to the 3. That is one quarter of a full circle. How many degrees did the hand turn?

A quarter of 360 is 360 ÷ 4 = 90. The hand turned through 90 one-degree angles, so 90 degrees.

Challenge!

The robot dog turns through 120 one-degree angles. Then it turns through 45 more in the same direction. What is the total measure of its turn?

Add the one-degree turns: 120 + 45 = 165. The whole turn measures 165 degrees.

Compare a 45-degree turn and a 90-degree turn. Where in real life might you see each one?

Great Work!

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correct

angle degree perpendicular determine analyze