Triangle Angle Relationships
A free Geometry lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Triangle angle theorems describe how angles inside and around triangles relate. The interior angles of every triangle add to 180 degrees, and an exterior angle equals the sum of the two remote interior angles. These facts matter because they let you solve for missing angles without measuring. When practicing, first decide whether the unknown angle is inside the triangle or outside it, then write an equation using the appropriate theorem. A common mistake is adding all visible angles together without identifying which angles form the triangle.
What you'll learn
- Use triangle angle sum
- Use exterior angles
- Solve triangle angle equations
Worked example
Problem. A triangle has angles 42 degrees and 68 degrees. Find the third angle.
- Triangle angles add to 180 degrees.
- 42 + 68 = 110.
- 180 - 110 = 70.
- Connect the result back to Triangle Angle Relationships so the geometric relationship is explicit.
Answer: 70 degrees
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. A triangle has angles 50 and 60 degrees. Find the third angle.
Show solution
- 50 + 60 = 110.
- 180 - 110 = 70.
Answer: 70
2. An equilateral triangle has each angle equal to what measure?
Show solution
- 180 divided by 3 is 60.
Answer: 60
3. A right triangle has one acute angle of 35 degrees. Find the other acute angle.
Show solution
- 90 - 35 = 55.
Answer: 55
4. An exterior angle is 124 degrees and one remote interior angle is 49 degrees. Find the other.
Show solution
- 124 - 49 = 75.
Answer: 75
5. Triangle angles are x, 2x, and 3x. Find x.
Show solution
- 6x = 180.
Answer: 30
Practice this interactively with instant feedback and an AI tutor.
Practice Triangle Angle Relationships Take the free placement check