# Video: Discovering Properties of Exterior Angles

Olivia is experimenting with the exterior angles of a triangle. She colors the angles, cuts them out, and sticks them together as seen in the figure. Will angle π§ fit in the space to complete the circle?

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### Video Transcript

Olivia is experimenting with the exterior angles of a triangle. She colours the angles, cuts them out, and sticks them together, as seen in the figure. Will angle π§ fit in the space to complete the circle?

Well, we actually know that the sum of the exterior angles of a triangle is equal to 360 degrees. So this actually suggests that yes, angle π§ will fit in the space, because weβve actually got the angles around a point which also equals 360 degrees. But letβs see if we can actually prove this and work this out.

So what Iβve done is Iβve actually marked the interior angles of our triangle on. So weβve got π, π, and π. Well, we know that π plus π plus π must be equal to 180 degrees because the interior angles of a triangle add up to 180. And we also know that the angles on a straight line is equal to 180 degrees. So therefore, we can actually write out what π, π, and π are in terms of π₯, π¦, and π§. Well, π is 180 minus π₯. π is 180 minus π¦. And π is 180 minus π§.

Okay, so now letβs try to add these together. Well, therefore, we can say that as π plus π plus π is equal to 180 degrees, then therefore 180 minus π₯ plus 180 minus π¦ plus 180 minus π§ must also be equal to 180. So therefore, if we can actually simplify, we get 540 minus π₯ minus π¦ minus π§ equals 180. So then if we actually add π₯, π¦, and π§ to both sides of the equation, we get 540 is equal to π₯ plus π¦ plus π§ plus 180.

And therefore, if we subtract 180 from each side, we get 360 is equal to π₯ plus π¦ plus π§. So therefore, yes this proves what we said at the beginning. The sum of the exterior angles of a triangle is equal to 360 degrees. And then as we said earlier, the angles around the point equal 364. So therefore, angle π§ will fit in the space.