Angles as Fractions of a Circle
 Exploring Angles in a Circle
 Introducing Angles as Fractional Parts of a Circle
 Angles as Fractional Parts of a Circle – Definition and Rules
 Angles as Fractional Parts of a Circle  Commonly Used Fractions
 How to Find Angles in a Circle?
 Angles in a Circle – Summary
 Frequently Asked Questions about Angles in a Circle
Basics on the topic Angles as Fractions of a Circle
Exploring Angles in a Circle
Have you ever thought about the thrilling rides at amusement parks and wondered how they relate to math? Join us on an imaginary Ferris wheel adventure, where we'll delve into the fascinating world of angles in a circle.
Introducing Angles as Fractional Parts of a Circle
Next time you find yourself on a Ferris wheel, consider how the concept of angles plays a role in this ride. Angles, circles and angles in a circle are everywhere, from the hands of a clock to the wheels of a car, and even in the thrilling rides at amusement parks.
Angles as Fractional Parts of a Circle – Definition and Rules
Let’s revise how angles occur first:
An angle is created when two rays meet at the same point at the center of a circle.
When an angle rotates or turns, a total of three hundred sixty degrees, it forms a circle. We can divide a circle into fractional parts and measure the degrees of those angles.
Angles as Fractional Parts of a Circle  Commonly Used Fractions
Understanding angles can be made easier by looking at fractions of a circle. A quarter turn of a circle forms a right angle that measures ninety degrees, a halfcircle measures one hundred eighty degrees, and threefourths equals two hundred seventy degrees.
Here is the table with commonly used angles that are expressed as fractions of a circle:
Fraction of a Circle  Parts in a Circle  Calculation  Angle size 

$\frac{1}{2}$  2  360÷2  180 degrees 
$\frac{1}{4}$  4  360÷4  90 degrees 
$\frac{3}{4}$  4  360÷4 = 90, 90 x 3 = 270  270 degrees 
Understanding Reflex Angles
Did you know there's a special type of angle called a reflex angle? These angles are greater than one hundred eighty degrees but less than three hundred sixty. They are intriguing and can be found in various shapes and patterns.
How to Find Angles in a Circle?
Calculating the degree of a fractional part of a circle is a fun puzzle to solve. Take the total degree of three hundred sixty and divide it by the number of parts, then multiply by the shaded parts. For example, fourtenths of three hundred sixty equals one hundred fortyfour degrees.
Take a look at the table for more examples of how to calculate angles that are fractional parts of a circle
Fraction of a Circle  Parts in a Circle  Shaded Parts  Calculation  Angle size 

$\frac{2}{6}$  6  2  360÷6= 60, 60 x 2 = 120  120 degrees 
$\frac{5}{8}$  8  5  360÷8 = 45, 45 x 5 = 225  225 degrees 
$\frac{4}{10}$  10  4  360÷10 = 36, 36 x 4 = 144  144 degrees 
Angles in a Circle – Summary
Angles and fractions aren't just in textbooks; they're part of everyday life. From the architectural marvels to the simple door hinge, you'll find angles everywhere. Try finding angles in circles and other circular objects around you and practice your newfound skills.
Following the video, there is additional practice with exercises and angles in a circle worksheet.
Angles as fractional parts of a circle is a fascinating concept that connects math with the world around us. Whether it's a thrilling Ferris wheel ride or the hands of a clock, angles are everywhere. Dive into this adventure, explore, and have fun learning!
Frequently Asked Questions about Angles in a Circle
Transcript Angles as Fractions of a Circle
"Nico, what's going on?" "The ride has stopped! "What are we going to do?" "Don't worry,(...) I have a plan to get us out of here!" As Nico and Nia begin their daring escape down from the Ferris Wheel, we can take a look at… “Angles as Fractions of a Circle.” An angle is created when two rays meet at the same point at the center of a circle. An angle can rotate clockwise OR counterclockwise. When an angle rotates or turns, a total of three hundred sixty degrees, it forms a circle. We can divide a circle into fractional parts and measure the degrees of those angles. First, let’s look at some benchmark fractions made by turns of a circle. This is onefourth of a circle. Look at the angle created by this quarter turn. Onefourth of a circle creates a right angle that measures ninety degrees. This is a halfcircle,(...) and the angle measures one hundred eighty degrees. Threefourths of a circle is equal to two hundredseventy degrees. This is also known as a REFLEX ANGLE. A reflex angle is any angle that is greater than one hundred eighty degrees, but less than three hundred sixty degrees. A full turn of the angle is a circle and measures three hundred sixty degrees. We can figure out the degrees of ANY fraction of a circle by solving for how many parts out of three hundred sixty degrees it covers. Let’s use Nico and Nia’s daring escape from the Ferris wheel to measure fractions of a circle. Their climb down has covered fourthtenths of the Ferris wheel. To solve for the degrees of this area, we are going to find fourtenths of three hundred sixty degrees. To start, we are going to take the three hundredsixty degrees angle turn... and divide it by the total number of parts. The circle is in ten parts. Three hundredsixty divided by ten equals thirtysix. This means each onetenth fraction has the value of thirtysix degrees. Now, we multiply the product by the numerator or shaded parts. There are four shaded parts. Thirtysix times four equals (...) one hundred fortyfour. Fourtenths of three hundredsixty is equal to one hundred fortyfour degrees. That means Nico and Nia turned one hundred fortyfour degrees on the Ferris Wheel. “Woah,(...) something is happening! HANG ON!” The Ferris wheel started moving counterclockwise and traveled backwards fivetwelfths of the circle. To solve for the number of degrees the wheel moved, we are going to find fivetwelfths of three hundredsixty. First, what is three hundredsixty divided by twelve? (...) It is thirty. Each fraction has the value of thirty degrees. Now, multiply thirty by the numerator, five. What is thirty times five? (...) One hundred fifty That means they went counterclockwise(...)One hundredfifty degrees. "This machine has gone haywire!" What fraction of the circle are we solving for? (...) We are finding threefifths of three hundredsixty. What do we do first? (...) We divide three hundredsixty by five. What is three hundred sixtyfive divided by five? (...) Seventytwo. What is the next step? (...) Multiply seventytwo by the numerator. What is seventytwo times three? (...) Two hundred sixteen degrees. Remember... an angle is created when two rays meet at the same point at the center of a circle. When an angle rotates or turns three hundred sixty degrees, it forms a circle. We can divide a circle into fractional parts and measure the degrees of those angles. To solve for the degree measurement of a fraction... First, divide three hundred sixty by the denominator, or number of parts the circle is divided into. Then, take the quotient and multiply it to the numerator, or number of shaded parts. [Nico and Nia near the bottom cart of the Ferris wheel, ready to jump and relieved they are safe. Just as they are about to leap off, the ride starts back up. Nico and Nia's eyes go wide! ” Here we go again!”
Angles as Fractions of a Circle exercise

Facts about circles.
HintsA half circle measures 180°.
A circle can be divided into several parts.
Solution A circle measures a total of 360°.
 An angle that measures greater than 180° but less than 360° is called a reflex angle.
 When an angle rotates 360° it forms a circle.
 A circle can be divided into fractional parts.
 Two rays meeting at the same point at the center of a circle form an angle.

Match the angles with the fractions.
HintsA circle can be divided into four equal parts.
The total turn of an angle to form a circle is 360°.
$\frac{1}{4}$ of a circle creates a right angle that measures 90°.
Solution 90° = $\frac{1}{4}$
 180° = $\frac{1}{2}$
 270° = $\frac{3}{4}$
 360°= $\frac{4}{4}$ or 1

Which statements are true?
Hints$\frac{1}{4}$ of a circle measures 90°.
A circle can be divided into several fractional parts.
A full circle measures 360°.
An angle is formed from the center of a circle.
There are four correct options.
Solution False: A circle is formed when an angle rotates a total of 270°.
 True: An angle can rotate clockwise or counterclockwise.
 False: A circle can only be divided into four fractional parts.
 True: A half circle measures 180°.
 True: A reflex angle is greater than 180° but less than 360°.
 True: An angle is formed by two rays meeting at a center point.

Can you figure out the angle of the Ferris wheel turning so far?
HintsThe circle is divided into ten parts and the fifth part is the best.
They would exit from the fifth part of the circle.
Multiply 36 with the numerator or the total number of shaded parts.
Solution They have to find $\frac{5}{10}$ of 360°.
 To start they divide 360 into 10 parts. Each part is 36°.
 Next they multiply 36 by 5, which equals 180°.
 So the angle at which they think they can safely exit is 180°.

How many degrees must an angle rotate to form a circle?
HintsAn angle can rotate clockwise or counterclockwise.
A half circle measures 180°
SolutionA circle measures 360°.

What is the angle measure of Nico's pizza?
HintsLook for the angle size of Nico's pizza which is $\frac{4}{12}$.
First divide 360 by 12. This will give you the degrees in one fractional part.
Multiply the measure of each angle with the numerator from Nico's fraction.
Solution Nico's pizza measures 120°
 To find $\frac{4}{12}$ of 360, first divide 360 by 12 to get 30
 Next multiply 30 by 4 to get 120