Prove that the interior angles of a triangle always add up to 180 degrees

Prove that the interior angles of a triangle always add up to 180 degrees.



In the drawing above the angles of the circles are equal and the angles of the squares are equal by properties of geometry.

Thus we can see that: circle + star + square = 180 degrees, or Pi Radians, since all 3 angles form a straight line.

We can use this fact to calculate the length of any angle in a triangle if we know the length of the other two angles.

Thus if
Angle 1 = 40 degrees
Angle 2 = 60 degrees

then angle 3 must equal 80 degrees to complete the sum of angles to 180 degrees.

similarly if
Angle 1 = Pi/4 radians
Angle 2 = Pi/4 radians

then Angle 3 must be equal to Pi/2 radians to complete the sum of angles to Pi.