What angle is called the outer corner of a triangle? Prove that the outer corner of the triangle is not adjacent to it.

Let’s start by recalling what the theorem sounds like: The outer angle of a triangle is equal to the sum of two angles of a triangle that are not adjacent to it.

Let us prove the theorem:

We are given a triangle ABC, the angles of the triangle are 1, 2 and 3, and 4 is the outer angle at the apex from angles 3.

Angle 3 and angle 4 are adjacent angles (the sum of adjacent angles is 180 °):

angle 3 + angle 4 = 180 °,

angle 4 = 180 ° – angle 3.

Also, the sum of the angles of the triangle is 180 °:

angle 1 + angle 2 + angle 3 = 180 °.

Therefore: angle 1 + angle 2 = 180 ° – angle 3;

angle 4 = angle 1 + angle 2.

Q.E.D.