The Angle Sum Theorem gives an important result about triangles, which is used in many algebra and geometry problems. We give the proof below.
Theorem: The sum of the measures of the interior angles of a triangle is 180°.
Prove: m1 + m2 + m3 = 180°
Construct a line parallel to through point Y. Call this line
|m1 + m5 = mAYX||Angle Addition Postulate|
|mAYX + m4 = 180°||Linear Pair Postulate|
|m1 + m5 + m4 = 180°||Substitution|
|Alternate Interior Angles Theorem|
m2 = m4
m3 = m5
|Definition of Congruence|
|m1 + m3 + m2 = 180°||Substitution|