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 find out about, “Angles as fractions of a circle.” An angle is created when two rays meet at the same point at the centre of a circle. An angle can rotate clockwise or anti-clockwise. When an angle rotates, or turns, a total of three hundred and 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 commonly used fractions made by turns of a circle. This is one-quarter of a circle. Look at the angle created by this quarter turn. One quarter of a circle creates a right angle that measures ninety degrees. This is half a circle and the angle measures one hundred and eighty degrees. Three-quarters of a circle is equal to two hundred and seventy degrees. This is also known as a reflex angle. A reflex angle is any angle that is greater than one hundred and eighty degrees, but less than three hundred and sixty degrees. A full turn of the angle is a circle and measures three hundred and sixty degrees. We can find the degrees of any fraction of a circle by solving how many parts out of three hundred and 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 fourth-tenths of the Ferris wheel. To find how many degrees this is, we are going to find four-tenths of three hundred and sixty degrees. To start with, we are going to take the three hundred and sixty degree angle turn and divide it by the total number of parts. The circle is in ten parts. Three hundred and sixty divided by ten equals thirty-six. This means each one- tenth fraction has the value of thirty-six degrees. Now, we multiply thirty six by how many parts are shaded. There are four shaded parts to show four tenths. Thirty-six times four equals one hundred and forty-four. Four-tenths of three hundred and sixty is equal to one hundred and forty-four degrees. That means Nico and Nia turned one hundred and forty-four degrees on the Ferris Wheel. “Woah, something is happening! Hang on!” The ferris wheel started moving anti-clockwise and travelled backwards five-twelfths of the circle. To solve how many degrees the wheel has moved, we are going to find five-twelfths of three hundred and sixty. First, what is three hundred and sixty 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 and fifty. That means they went anti-clockwise one hundred and fifty degrees. "This machine has gone haywire!" What fraction of the circle are we finding?We are finding three-fifths of three hundred and sixty. What do we do first? We divide three hundred and sixty by five. What is three hundred and sixty divided by five? Seventy-two. What is the next step? Multiply seventy-two by the numerator. What is seventy-two times three? Two hundred and sixteen degrees. Remember, an angle is created when two rays meet at the same point at the centre of a circle. When an angle rotates, or turns, three hundred and sixty degrees, it forms a circle. We can divide a circle into fractional parts and measure the degrees of those angles. To solve how many degrees are in the fraction: first, divide three hundred and sixty by the denominator, or number of parts the circle is divided into. Then, take the quotient and multiply it with the numerator, or number of shaded parts.” Here we go again!”