### 7-4: Exterior Angles of Triangles

#### Part 1

Intro

An exterior angle of a triangle is an angle formed by a side and an extension of an adjacent side. ∠1 is an exterior angle of each triangle.

For each exterior angle of a triangle, the two nonadjacent interior angles are its remote interior angles. ∠2 and ∠3 are remote interior angles of ∠1 in each triangle. Example Identifying Interior and Exterior Angles of Triangles

• a. Which of the numbered angles are exterior angles?

• b. Name the remote interior angles for each exterior angle.

• c. Which exterior angles are congruent? Explain. Solution

• a. Angles 1, 3, 8, and 9 are exterior angles of the triangle because they are angles formed by a side and an extension of an adjacent side.

• b. Angles 5 and 6 are the remote interior angles for angle 1.

Angles 5 and 6 are the remote interior angles for angle 3.

Angles 4 and 5 are the remote interior angles for angle 9.

Angles 4 and 6 are the remote interior angles for angle 8.

• c. Angles 1 and 3 are vertical angles. Vertical angles have equal measures, so they are congruent.

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