Exterior angle property

Key notes:

The measure of an exterior angle of a triangle equals the sum of the two remote interior angle measures.

∠2 = ∠3 + ∠4

Exterior Angle Property

1. Definition of Exterior Angle:
   • An exterior angle is formed when a side of a polygon is extended. It is the angle between the extended side and the adjacent side.
2. Exterior Angle Theorem:
   • The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
   • Mathematically: If ∠D is an exterior angle, then ∠D = ∠A + ∠B (where ∠A and ∠B are the interior angles opposite to the exterior angle).
3. Application:
   • This property helps in finding unknown angles in triangles, which is useful in solving geometry problems.
4. Example: Consider triangle ABC with an exterior angle at vertex C, denoted as angle D. If angle A = 40° and angle B = 60°, then:

∠D = ∠A + ∠B = 40° + 60° = 100°.