11.07 Angles within a circle
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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.
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Question 1
An angle of $90^\circ$90° is shown in the circle below.
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