Exterior angle property

key notes :

Definition:

An exterior angle of a triangle is formed when one side of the triangle is extended, creating an angle outside the triangle.

Exterior Angle Theorem:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

  • Formula:

Example:

  • Consider triangle ABC, where an exterior angle is formed by extending side BC. The exterior angle at vertex A equals the sum of the interior angles at vertices B and C.

Properties:

  • This property holds for any triangle (scalene, isosceles, or equilateral).
  • The exterior angle is always larger than either of the two non-adjacent interior angles.

Practical Uses:

  • This property is useful for solving problems related to angles in polygons, geometry proofs, and constructions.

Example Problem:

  • If the interior angles at vertices B and C of triangle ABC are 40° and 50°, respectively, then the exterior angle at vertex A is:
  • Therefore, the exterior angle at vertex A is 90°.

Learn with an example

What is ∠1?

∠1 = ______°

∠1 is an exterior angle of the triangle. The two remote interior angles measure 79° and 63°.

To find the exterior angle measure, add the two remote interior angle measures.

∠1 = 79°+63°

= 142° Add

So, ∠1 = 142°.

What is ∠1?

∠1 = ___°

∠1 is an exterior angle of the triangle. The two remote interior angles measure 64° and 66°.

To find the exterior angle measure, add the two remote interior angle measures.

∠1 = 64°+66°

= 130° Add

So, ∠1 = 130°.

What is ∠1?

∠1 = ____°

∠1 is an exterior angle of the triangle. The two remote interior angles measure 47° and 94°.

To find the exterior angle measure, add the two remote interior angle measures.

∠1 = 47°+94°

= 141° Add

So, ∠1 = 141°.

Let’s practice!