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.