Chapter 3, Problem 31CUR

To determine

To state: the postulate or theorem which justifies the given statement, “ $m\angle AEB=m\angle 2+m\angle C$ ”

Answer to Problem 31CUR

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-12: The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.

Consider the given figure:

Consider the triangle $△BEC$ ,

For the triangle $△BEC$ , the angle $\angle AEB$ is an exterior angle.

So, by theorem 3-12, the measure of the exterior angle $\angle AEB$ of the triangle $△BEC$ equals the sum of the measures of the two remote interior angles which in this case are $\angle 2$ and $\angle C$ .

That is,

  $m\angle AEB=m\angle 2+m\angle C$