Question

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.

Answer 1

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°