# Alternate Interior Angles

- Author:
- Maurice OReilly

"Alternate interior angles are equal."
Check .
Given and is the sum of the green, purple and red angles.
But the angles in the triangle are these green, purple and red angles.
So the sum of the angles in any triangles is 180 .

**here**for an explanation of alternate interior angles. This is all we need to prove that the sum of the angles in any triangle is 180__any__triangle, ABC. Then draw a line through A parallel to the side BC, as shown. The two green angles (at A & C) are alternate interior angles, and so they are equal. The two purple angles (at A & B) are alternate interior angles, and so they are equal. The straight angle at A is 180