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Exterior Angle Theorem

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About This Diagram

This visualization demonstrates the Exterior Angle Theorem with two views: a detailed single example and a comparison showing all three vertices.

Exterior Angle Theorem

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

\[m\angle_{exterior} = m\angle_{remote_1} + m\angle_{remote_2}\]

Key Terms

Term Definition
Exterior angle An angle formed when one side of a triangle is extended
Remote interior angles The two interior angles NOT adjacent to the exterior angle
Adjacent interior angle The interior angle that forms a linear pair with the exterior angle

Example Calculation

For a triangle with angles 50°, 60°, and 70°: - Exterior angle at C = ∠A + ∠B = 50° + 60° = 110° - Check: 110° + 70° = 180° (linear pair)

Key Facts

  • An exterior angle is always larger than either remote interior angle
  • The exterior angle and adjacent interior angle form a linear pair (sum to 180°)

Interaction

Click anywhere to toggle between the basic example and the view showing all three exterior angles.

Learning Objectives

  • Understand the relationship between exterior and remote interior angles
  • Apply the Exterior Angle Theorem to find missing angles

Bloom's Taxonomy Level

Understanding and Applying

Iframe Embed Code

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