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9.02 Angles within a circle

Lesson

Are you ready?

Do you remember how to compare and order fractions?

If I have $2$2 thirds, how many more thirds do I need to make a whole?

Learn

When two rays or line segments share a common endpoint, they form an angle between them.

An angle formed by two line segments

We can construct an angle by using two line segments that meet at the center of a circle.

An angle at the center of a circle

In this way, we can form angles that turn through fractions of a circle.

An angle that is $\frac{1}{4}$14 of a full circle

A special angle is formed by turning through $\frac{1}{360}$1360 of a circle. We define the size of this angle to be one degree, which can be written as $1^\circ$1°.

An angle that is $\frac{1}{360}$1360 of a full circle. This angle measures $1^\circ$1° in size.

We can use this to measure the size of any angle.

For example, an angle which turns through $\frac{10}{360}$10360 of a circle is $10$10 times as large as a $1^\circ$1° angle. We can think of this angle as having turned through $10$10 one degree angles, and so it has a measure of $10^\circ$10°.

An angle that is $\frac{10}{360}$10360 of a full circle. This angle measures $10^\circ$10° in size.

Apply

Question 1

An angle of $90^\circ$90° is shown in the circle below.

  1. What fraction of a full circle is this angle?

    $\frac{1}{3}$13

    A

    $\frac{1}{4}$14

    B

    $\frac{1}{6}$16

    C

    $\frac{1}{8}$18

    D

Remember!
An angle that turns through $\frac{1}{360}$1360 of a full circle is called a "one degree angle", and we write the size of this angle as $1^\circ$1°.
We can then compare other angles to this to measure the size of any angle!

Outcomes

4.MD.C.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint; and understand concepts of angle measurement.

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