NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Triangle and polygon angles

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Required skills (click to reveal)

A regular pentagon is inscribed in a circle. Using the fact that the sum of the interior angles of an n-sided polygon is (n-2) × 180°, determine the exact measure, in degrees, of one interior angle of the pentagon.

Show your reasoning by first calculating the total interior angle sum, then dividing by 5. Provide the exact answer as a fraction if necessary.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. A regular pentagon has 5 sides, so n = 5.
  2. The sum of the interior angles of an n-sided polygon is given by the formula: (n - 2) × 180°.
  3. Substitute n = 5 into the formula: (5 - 2) × 180°.
  4. Calculate the difference: 5 - 2 = 3.
  5. Multiply: 3 × 180° = 540°.
  6. The total interior angle sum is 540°.
  7. Since the pentagon is regular, all interior angles are equal.
  8. To find one interior angle, divide the total sum by 5: 540° ÷ 5.
  9. Perform the division: 540 ÷ 5 = 108.
  10. The measure of one interior angle is 108°.
  11. Check: 5 × 108° = 540°, which matches the total sum.
  12. Therefore, one interior angle of the regular pentagon is exactly 108°.

Reference answer: 108°

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