Exterior Angle Theorem

Front

What is the Exterior Angle Theorem?

Back

The Exterior Angle Theorem 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.

Front

How do you calculate the measure of an exterior angle in a triangle?

Back

To calculate the measure of an exterior angle, add the measures of the two opposite interior angles.

Front

If one interior angle of a triangle is 40° and another is 70°, what is the measure of the exterior angle adjacent to the 70° angle?

Back

The exterior angle is 40° + 70° = 110°.

Front

What is the relationship between interior angles and exterior angles in a triangle?

Back

The sum of the measures of the interior angles of a triangle is always 180°, and each exterior angle is equal to the sum of the two opposite interior angles.

Front

If angle A = 50° and angle B = 60°, what is the measure of angle C in triangle ABC?

Back

Angle C = 180° - (50° + 60°) = 70°.

Front

What is the sum of the exterior angles of any polygon?

Back

The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides.

Front

In triangle XYZ, if angle X = 30° and angle Y = 50°, what is the measure of the exterior angle at vertex Z?

Back

The exterior angle at vertex Z is 30° + 50° = 80°.

Front

How can you find a missing angle in a triangle using the Exterior Angle Theorem?

Back

You can find a missing angle by using the formula: Missing angle = Exterior angle - adjacent interior angle.

Front

What is the measure of an exterior angle if the two opposite interior angles are 45° and 55°?

Back

The measure of the exterior angle is 45° + 55° = 100°.

Front

If an exterior angle measures 120°, what are the possible measures of the two opposite interior angles?

Back

The two opposite interior angles must sum to 120°; for example, they could be 60° and 60° or 70° and 50°.