Exterior Angle Theorem

Learning Objectives Define an exterior angle of a triangle and identify its corresponding remote interior angles. State the Exterior Angle Theorem in words and as a formula. Apply the Exterior Angle Theorem to calculate the measure of an unknown exterior angle. Use the Exterior Angle Theorem to find the measure of an unknown remote interior angle. Set up and solve linear algebraic equations involving the angles of a triangle using the theorem. Explain the relationship between the Exterior Angle Theorem and the Triangle Sum Theorem. Ever wondered how a skateboard ramp designer calculates the perfect angle for a smooth transition? 🛹 It's all about understanding the angles outside a triangle! This tutorial will introduce you to the Exterior Angle Theorem, a powerful shor...

TermDefinitionExample TriangleA closed, two-dimensional figure with three straight sides and three angles.A shape with vertices A, B, and C is called triangle ABC. Interior AngleAn angle located on the inside of a triangle, formed by two of its sides.In triangle ABC, the angles ∠A, ∠B, and ∠C are all interior angles. Exterior AngleAn angle formed by extending one side of a triangle. It is outside the triangle and adjacent to an interior angle.If you extend side BC of triangle ABC to a point D, the angle ∠ACD is an exterior angle. Adjacent Interior AngleThe interior angle that forms a linear pair (adds up to 180°) with a specific exterior angle.For the exterior angle ∠ACD, the adjacent interior angle is ∠ACB. Remote Interior AnglesThe two interior angles of a triangle that are not adjacent...

Exterior Angle Theorem m∠Exterior = m∠Remote_1 + m∠Remote_2 The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. This is the main shortcut for solving these types of problems. Triangle Sum Theorem m∠A + m∠B + m∠C = 180° The sum of the measures of the three interior angles of any triangle is always 180°. This theorem is used to prove the Exterior Angle Theorem.