Hi there! Today I’d like to discuss two theories that I learned about in Math class this year: the Interior Angle Theory and the Exterior Angle Theory. 

The Interior Angle Theory states that when the value of the 3 interior angles inside a triangle are added together, they will total exactly 180 degrees. I’ve tested this out with this triangle:

While the angles on this computer-drawn triangle may not be completely accurate, this triangle proves that the three angles add up to 180 degrees.

The second theory that I wanted to talk about is the Exterior Angle Theory. This theory states that the value of an exterior angle is equal to the sum of the two opposite interior angles. For example:

 

 

We start by completing a multi-step equation with the exterior angle on one side and the interior angle on the other. We then solve like normal to get the value of x. Then, we find the value of the exterior angle by substituting for x which proves that they are indeed equal.

Using the above diagrams, solve each of the problems below. For the interior angle theory, tell whether the triangle supports the theory. For the exterior angle theory, find the value of x and solve for the exterior angle. Check your answers on July 2.

Thanks for reading!

Gabe