The Exterior Angle Theorem is a key concept in geometry. It states that:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Example:

If you have a triangle with interior angles $\angle A$, $\angle B$, and $\angle C$, and you extend the side opposite $\angle C$, creating an exterior angle $\angle D$, then according to the Exterior Angle Theorem: $\angle D = \angle A + \angle B$

Application Steps:

1. Identify the exterior angle of the triangle.
2. Find the two non-adjacent interior angles.
3. Use the theorem to set up the equation: Exterior angle = Sum of the two non-adjacent interior angles.
4. Solve for the unknown angle if needed.

Example Problem:

In a triangle, if one exterior angle is $120^\circ$ and one of the opposite interior angles is $45^\circ$, find the other interior angle.

• By the theorem: $120^\circ = 45^\circ + \text{other interior angle}$.
• Solving: $\text{other interior angle} = 120^\circ - 45^\circ = 75^\circ$.

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Relative Questions:

1. How do you calculate interior angles of a triangle using exterior angles?
2. Can the Exterior Angle Theorem apply to polygons other than triangles?