Exterior Angle Property

 

ABOUT:

The Angle formed by a side with its extended adjacent side of a triangle is called an exterior angle of the triangle.

Exterior Angle Property states that the measure of exterior angles of a triangle is equal to the sum of its two interior opposite angles.

A triangle has three corners, called vertices.

The sides of a triangle (line segments) that come together at a vertex form two angles

Only one of these angles contains the third side of the triangle in its interior, and this angle is called an interior angle of the triangle.

In the figure below, the angles ABCBCA and CAB are the three interior angles of the triangle.

An exterior angle is formed by extending one of the sides of the triangle;

The angle between the extended side and the other side is the exterior angle. In the figure below, angle ACD is an exterior angle.

Properties

  • An exterior angle of a triangle is equal to the sum of the opposite interior angles.
  • If the equivalent angle is taken at each vertex, the exterior angles always add to 360° .