Question 389290
a: The angles of a triangle always add up to 180 degrees.

b: 4 is an exterior angle.

c: Angles that are supplementary add up to 180 degrees.

d: 180 = 180

e: Subtract the measure of angle 3 from both sides of the equality.


The way I would prove this uses the same steps, but is much shorter and just as concise. Suppose that angle 1 and angle 2 measure {{{alpha}}} and {{{beta}}} respectively. Since angle 1 + angle 2 + angle 3 = 180, then angle 3 = 180 - angle 1 - angle 2 = {{{180 - alpha - beta}}}. 


Since angle 3 + angle 4 = 180, angle 4 = 180 - angle 3 = {{{180 - (180 - alpha - beta) = alpha + beta}}} which is the same as angle 1 + angle 2.