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Remote Interior Angles - Problem 1 3,076 views

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

The measure of an exterior angle can be found with the values of the remote interior angles. The remote interior angles are the angles inside of the triangle that are not adjacent to the desired exterior angle.

This exterior angle's measure is the sum of the remote interior angle). This is because from the triangle angle sum theorem that the sum of the angles inside a triangle is 180°, and the sum of a linear pair (two adjacent angles that lie on the same line) is also 180°. As a result, since the adjacent interior angle is 180° - the sum of the remote interior angles, and it is also 180° - the exterior angle, the measure of the exterior angle is the same as the sum of the remote interior angles.

We can use remote interior angles to find missing angles. So if we look here x is an exterior angle and 90 degrees and 35 are the more interior angles.

So let’s start by saying x degrees must equal 90 plus 35. Well, that’s pretty simple. 90 and one 35, is 125. So I can erase x and I know that this is 125 degrees. To find y, I can say that 125 and y must be a linear pair or supplementary, which means y plus 125 equals 180 degrees. So we’ll subtract 125 degrees from both sides and we see that y has to be 55 degrees.

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