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Regular Polygon Angles Worksheets

Find one interior angle, one exterior angle and the interior-angle sum for regular polygons with five through twelve sides.

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Find one interior angle, one exterior angle and the interior-angle sum. Round individual angles to the nearest tenth when needed.

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Keep three angle quantities separate

The interior-angle sum covers every interior angle. Divide that sum by n for one interior angle; divide 360 degrees by n for one exterior angle.

Learning objective

What this activity builds

Distinguish an angle sum from one interior or exterior angle of a regular polygon.

Worked example

Find one interior angle, one exterior angle and the interior-angle sum of a regular hexagon.

120°, 60° and 720°.

With n = 6, the sum is (6 − 2) × 180° = 720°. Divide by 6 for one interior angle; 360° ÷ 6 gives one exterior angle.

Teaching notes

Make the practice count

  • For a simple polygon with n sides, the interior-angle sum is (n − 2) × 180°.
  • Only a regular polygon has all interior angles equal, allowing division by n.
  • One interior angle and its adjacent exterior angle add to 180°.

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Twelve diagrams ask for one interior angle, one exterior angle and the interior-angle sum. Exact fractions and explicit nearest-tenth approximations appear on the key when needed.

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Math SheetNameScoreTeacherDateAngles in Regular PolygonsFind one interior angle, one exterior angle, and the sum of the interior angles. Round individual angles to the nearest tenth when needed.1. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:2. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:3. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:4. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:5. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:6. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:For a regular n-gon: sum = 180(n - 2), interior = sum/n, exterior = 360/n.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateAngles in Regular PolygonsFind one interior angle, one exterior angle, and the sum of the interior angles. Round individual angles to the nearest tenth when needed.7. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:8. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:9. Find one interior angle, one exterior angle, and the sum of the interior angles.Interior angle:Exterior angle:Interior-angle sum:10. Find one interior angle, one exterior angle, and the sum of the interiorangles.Interior angle:Exterior angle:Interior-angle sum:11. Find one interior angle, one exterior angle, and the sum of the interiorangles.Interior angle:Exterior angle:Interior-angle sum:12. Find one interior angle, one exterior angle, and the sum of the interiorangles.Interior angle:Exterior angle:Interior-angle sum:For a regular n-gon: sum = 180(n - 2), interior = sum/n, exterior = 360/n.math-sheet.comPage 2 of 2

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