7.03 Exterior angles of triangles

Lesson

Practice

Introduction

We've looked at parallel lines and transversals and angles in triangles . We can use that knowledge to extend what we know to exterior angles of a triangle.

Ideas

Exterior angles of a triangle

Exterior angles of a triangle

The angles formed outside the triangle by extending the sides are called exterior angles. The size of an exterior angle is always equal to the sum of the internal angles on the opposite side.

Examples

Example 1

Solve for the value of h in the diagram below.

This image shows two interior angles of a triangle measuring 40 degrees and 63 degrees and an exterior angle with missing angle measure of h degrees.

Worked Solution

Create a strategy

Equate the sum of the interior angles to the opposite exterior angle.

Apply the idea

\displaystyle h	\displaystyle =	\displaystyle 40\degree +63 \degree	Add the interior angles
	\displaystyle =	\displaystyle 103\degree	Evaluate

Example 2

Solve for the value of x in the diagram below.

Triangle with interior angles of 52 and x degrees and exterior angle of 108 degrees.

Worked Solution

Create a strategy

Equate the sum of the interior angles to the opposite exterior angle.

Apply the idea

\displaystyle x+52	\displaystyle =	\displaystyle 108	Add the interior angles and equate to 108
\displaystyle x+52-52	\displaystyle =	\displaystyle 108-52	Subtract 52 from both sides
\displaystyle x	\displaystyle =	\displaystyle 56\degree	Evaluate

Idea summary

An exterior angle is equal to the sum of the opposite interior angles.

Outcomes

8.G.A.5

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.