4.2. Exterior Angles Theorems http://www.ck12.org
Guidance
Anexterior angleis the angle formed by one side of a polygon and the extension of the adjacent side. In all
polygons, there aretwosets of exterior angles, one going around the polygon clockwise and the other goes around
the polygon counterclockwise. By the definition, the interior angle and its adjacent exterior angle form a linear pair.
TheExterior Angle Sum Theoremstates that each set of exterior angles of a polygon add up to 360◦.
m^61 +m^62 +m^63 = 360 ◦
m^64 +m^65 +m^66 = 360 ◦Remote interior anglesare the two angles in a triangle that are not adjacent to the indicated exterior angle.^6 Aand
(^6) Bare the remote interior angles for exterior angle (^6) ACD.
TheExterior Angle Theoremstates that the sum of the remote interior angles is equal to the non-adjacent exterior
angle. From the picture above, this means thatm^6 A+m^6 B=m^6 ACD. Here is the proof of the Exterior Angle
Theorem. From the proof, you can see that this theorem is a combination of the Triangle Sum Theorem and the
Linear Pair Postulate.
Given: 4 ABCwith exterior angle^6 ACD
Prove:m^6 A+m^6 B=m^6 ACD