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Remote Interior Angles - Problem 2 2,556 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

Given the measure of the exterior angle and one remote interior angle of a triangle, it is possible to find the measure of the other remote interior angle. Remember that the measure of the exterior angle is the sum of the remote interior angles. So, the measure of the unknown interior angle is the measure of the exterior angle minus the measure of the other interior angle.

To clarify, let one remote interior angle be R°, the exterior angle be E° and the unknown remote interior angle be x°. Since E° = R° + x°, you know that x° = E° - R°. Plug in the values of the exterior angle and known remote interior angle.

If you know the exterior angle and you know one of the remote interior angles, then you can just set up a simple equation to find x.

We know that 125 degrees has to equal the sum of the two remote interior angles, which is 50 degrees and x degrees. So we just have a simple equation to solve, subtract 50 degrees and we see that x must be 75 degrees.