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Exercise C. Find each measure of the interior angle given the number of sides of a regular polygon.

3
24
30
15
5


Sagot :

Answer:

Measure of each interior angles

  1. 3 sides = 60°
  2. 24 sides = 165°
  3. 30 sides = 168°
  4. 15 sides = 156°
  5. 5 sides = 108°

Step-by-step explanation:

Formula for the sum of the interior angle

  • (n-2) × 180

Formula for each interior angle

  • [(n-2) × 180] ÷ n

Solution:

3 sides

  • [(3-2) × 180] ÷ 3
  • [1 × 180] ÷ 3
  • 180° ÷ 3
  • 60°

24 sides

  • [(24-2) × 180] ÷ 24
  • [22 × 180] ÷ 24
  • 3960° ÷ 24
  • 165°

30 sides

  • [(30-2) × 180] ÷ 30
  • [28 × 180] ÷ 30
  • 5040° ÷ 30
  • 168°

15 sides

  • [(15-2) × 180] ÷ 15
  • [13 × 180] ÷ 15
  • 2340° ÷ 15
  • 156°

5 sides

  • [(5-2) × 180] ÷ 5
  • [3 × 180] ÷ 5
  • 540° ÷ 5
  • 108°
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