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Mhanifa please help!
Question 1: Find the sum of the measures of the interior angles of a heptagon.
Question 2: The sum of the measures of the interior angles of a convex polygon is 3060°. Classify the polygon by the number of sides.
Question 3: Find the measure of each interior and exterior angle of a regular 30-gon.

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mhanifa

Answer:

Sum of interior angles of a regular polygon:

  • S = (n - 2)*180°

Question 1:

Heptagon has 7 sides

Sum of interior angles:

  • S = (7 - 2)*180° = 5*180° = 900°

Question 2:

S = 3060°, n = ?

  • (n - 2)*180° = 3060°
  • n - 2 = 3060°/180°
  • n - 2 = 17
  • n = 19

19-sided polygon (Enneadecagon)

Question 3:  

Let each angle be x

  • 30x = (30 - 2)*180°
  • x = (30 - 2)*6°
  • x = 28*6
  • x = 168°

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