Measuring Angles in Triangles
Overview
The interior angles of every triangle add to 180°, and that one fact drives everything in this lesson. Extending a side of a triangle creates an exterior angle whose measure equals the sum of the two remote interior angles, which turns many two-step problems into one-step problems. A third result, the Third Angle Theorem, says that if two angles of one triangle are congruent to two angles of another triangle, the remaining angles must be congruent as well.
Vocabulary
- Angle Sum Theorem
- The theorem stating that the measures of the three interior angles of a triangle always add to 180°.
- Exterior Angle
- An angle formed outside a triangle when one side of the triangle is extended. The exterior angle and the interior angle next to it form a linear pair, so they are supplementary.
- Remote Interior Angles
- The two interior angles of a triangle that are not adjacent to a given exterior angle — they are the angles in the two far corners of the triangle.
- Exterior Angle Theorem
- The theorem stating that the measure of an exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
- Third Angle Theorem
- The theorem stating that if two angles of one triangle are congruent to two angles of another triangle, then the third angles of the two triangles are also congruent.
Main Ideas
- Angle Sum Theorem: in any triangle, the three interior angle measures add to 180°. Given two angles, subtract their sum from 180° to get the third.
- Exterior Angle Theorem: an exterior angle equals the sum of its two remote interior angles — no need to find the adjacent angle first.
- An exterior angle and its adjacent interior angle are supplementary (they form a linear pair), so each can be found from the other by subtracting from 180°.
- Third Angle Theorem: two matching angle pairs between two triangles force the third pair to be congruent, because both third angles are what remains of 180°.
- With expressions, choose the theorem that fits the picture: angle measures inside one triangle add to 180°, while an exterior angle equals the sum of the two remote interiors.
Lesson Notes
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Lesson Video
Watch the lesson video.
Interactive Activity
Use the angle sums of a triangle and the exterior angle relationship to build missing measures.
Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.