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.

Three triangles, each with interior angles 2 and 3. In each triangle, a side extends beyond the third vertex, forming exterior angle 1 with the other side.

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.

Angles of a triangle.

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.


End ofPage 242

Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties