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 one-fourth of a circle. Look at the angle created by this quarter turn. One-fourth of a circle creates a right angle that measures ninety degrees. This is a half-circle,(...) and the angle measures one hundred eighty degrees. Three-fourths of a circle is equal to two hundred-seventy 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 fourth-tenths of the Ferris wheel. To solve for the degrees of this area, we are going to find four-tenths of three hundred sixty degrees. To start, we are going to take the three hundred-sixty degrees angle turn... and divide it by the total number of parts. The circle is in ten parts. Three hundred-sixty divided by ten equals thirty-six. This means each one-tenth fraction has the value of thirty-six degrees. Now, we multiply the product by the numerator or shaded parts. There are four shaded parts. Thirty-six times four equals (...) one hundred forty-four. Four-tenths of three hundred-sixty is equal to one hundred forty-four degrees. That means Nico and Nia turned one hundred forty-four degrees on the Ferris Wheel. “Woah,(...) something is happening! HANG ON!” The Ferris wheel started moving counterclockwise and traveled backwards five-twelfths of the circle. To solve for the number of degrees the wheel moved, we are going to find five-twelfths of three hundred-sixty. First, what is three hundred-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 fifty That means they went counterclockwise(...)One hundred-fifty degrees. "This machine has gone haywire!" What fraction of the circle are we solving for? (...) We are finding three-fifths of three hundred-sixty. What do we do first? (...) We divide three hundred-sixty by five. What is three hundred sixty-five divided by five? (...) Seventy-two. What is the next step? (...) Multiply seventy-two by the numerator. What is seventy-two 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!”