Answered

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how many sides does a regular polygon have if the interior angle of a regular polygon is 162° degrees? ​

Sagot :

✒MATHEMATICS

SOLUTION :

Let n be the number of sides So,

  • Sum = (n - 2) × 180°
  • Sum = 180°n - 360°

Since each interior angle is 162°, then,

  • 162° = sum/n
  • 162° = 180°n - 360°/n
  • 162°n = 180°n - 360°
  • 360° = 180°n - 162°n
  • 18°n = 360°
  • n = 360°/18°
  • n = [tex]{\boxed{\green{\sf{20° }}}}[/tex]

ANSWER :

  • Therefore, number of sides of given polygon is 20 sides.

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