Polygon Angle Sums
A free Geometry lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
A polygon with n sides can be split into n - 2 triangles, so its interior angle sum is (n - 2) x 180 degrees. One exterior angle at each vertex always adds to 360 degrees. In Geometry Foundations, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Use the polygon interior angle sum formula
- Find one angle in regular polygons
- Use exterior angle sums
Worked example
Problem. Find the interior angle sum of a hexagon.
- A hexagon has 6 sides.
- Use (n - 2) x 180.
- (6 - 2) x 180 = 720.
- Connect the result back to Polygon Angle Sums so the geometric relationship is explicit.
Answer: 720 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. Find the interior angle sum of a quadrilateral.
Show solution
- Use (4 - 2) x 180.
Answer: 360
2. Find the interior angle sum of a pentagon.
Show solution
- Use (5 - 2) x 180.
Answer: 540
3. Find the interior angle sum of an octagon.
Show solution
- Use (8 - 2) x 180.
Answer: 1080
4. A regular hexagon has each interior angle equal to what measure?
Show solution
- Hexagon sum is 720.
- 720 divided by 6 is 120.
Answer: 120
5. A regular polygon has 10 sides. What is each exterior angle?
Show solution
- Exterior angles add to 360.
- 360 divided by 10 is 36.
Answer: 36
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