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Polygon Angle Sums — Easy Worksheet 2
Grade 10 · MathSheets Name: ____________________ Date: __________
Solve each problem.
How to solve
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Example
Find the sum of the interior angles of a polygon with 6 sides.
Answer: 720
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (4 − 2) × 180° = 2 × 180° = 360°.
✓ Correct!
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (4 − 2) × 180° = 2 × 180° = 360°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 8 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (3 − 2) × 180° = 1 × 180° = 180°. A regular polygon has 3 equal angles, so each one is 180° ÷ 3 = 60°.
✓ Correct!
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (3 − 2) × 180° = 1 × 180° = 180°. A regular polygon has 3 equal angles, so each one is 180° ÷ 3 = 60°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 6 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The exterior angles of any polygon add to 360°. A regular polygon has 5 equal exterior angles, so each one is 360° ÷ 5 = 72°.
✓ Correct!
Not quite. The answer is
💡 The exterior angles of any polygon add to 360°. A regular polygon has 5 equal exterior angles, so each one is 360° ÷ 5 = 72°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 8 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The angles of a triangle add to (3 − 2) × 180° = 180°. So the third angle is 180° − 90° − 52° = 38°.
✓ Correct!
Not quite. The answer is
💡 The angles of a triangle add to (3 − 2) × 180° = 180°. So the third angle is 180° − 90° − 52° = 38°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 4 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (5 − 2) × 180° = 3 × 180° = 540°.
✓ Correct!
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (5 − 2) × 180° = 3 × 180° = 540°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 3 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (8 − 2) × 180° = 6 × 180° = 1,080°. A regular polygon has 8 equal angles, so each one is 1,080° ÷ 8 = 135°.
✓ Correct!
Not quite. The answer is
💡 By the Polygon Angle Sum Theorem, the interior angles add to (n − 2) × 180° = (8 − 2) × 180° = 6 × 180° = 1,080°. A regular polygon has 8 equal angles, so each one is 1,080° ÷ 8 = 135°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 5 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The exterior angles of any polygon add to 360°. A regular polygon has 3 equal exterior angles, so each one is 360° ÷ 3 = 120°.
✓ Correct!
Not quite. The answer is
💡 The exterior angles of any polygon add to 360°. A regular polygon has 3 equal exterior angles, so each one is 360° ÷ 3 = 120°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 4 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The angles of a quadrilateral add to (4 − 2) × 180° = 360°. So the fourth angle is 360° − 76° − 46° − 69° = 169°.
✓ Correct!
Not quite. The answer is
💡 The angles of a quadrilateral add to (4 − 2) × 180° = 360°. So the fourth angle is 360° − 76° − 46° − 69° = 169°.
💡 How to solve: Polygon Angle Sums
The interior angles of an n-sided polygon add to (n - 2) × 180°. For a regular polygon, each interior angle = (n - 2) × 180° ÷ n and each exterior angle = 360° ÷ n. For a triangle subtract the known angles from 180°, and for a quadrilateral subtract them from 360°.
Try a similar one
Find the sum of the interior angles of a polygon with 8 sides.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Polygon Angle Sums — Easy Worksheet 2
Solve each problem.