Angle Sum of a Triangle

Examples, videos, and solutions to help Grade 8 students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180°.

Students present informal arguments to draw conclusions about the angle sum of a triangle.

New York State Common Core Math Grade 8, Module 2, Lesson 14

Worksheets for Grade 8

Student Outcomes
• Students know a third informal proof of the angle sum theorem.
• Students know how to find missing interior and exterior angle measures of triangles and present informal arguments to prove their answer is correct.

Lesson Summary
The sum of the remote interior angles of a triangle is equal to the measure of the exterior angle.

Classwork Discussion
Students will see one final informal proof of the angle sum of a triangle before moving on to working with exterior angles of triangles.

Now let’s look at what is called the exterior angle of a triangle. An exterior angle is formed when one of the sides of the triangle is extended. The interior angles are inside the triangle, so the exterior angle is outside of the triangle along the extended side.

Exercises 1 - 4
Use the diagram below to complete Exercises 1 - 4.

1. Name an exterior angle and the related remote interior angles.
   
2. Name a second exterior angle and the related remote interior angles.
   
3. Name a third exterior angle and the related remote interior angles.
   
4. Show that the measure of an exterior angle is equal to the sum of the related remote interior angles.

Example 1 - 4
Find the measure of angle x.

Exercise 5 - 10
5. Find the measure of angle. Present an informal argument showing that your answer is correct.

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