find the measure of each angle of a regular heptagon?

Answer 1

The sum of the angles of a polygon with N sides is 180 * (N-2). So the sum of the angles of a triangle is 180*(3-2) = 180. For a quadrilateral, it's 180*(4-2) = 360.

For a regular polygon, the N angles are all equal, so each angle is that quantity divided by N. Thus, each angle for a regular polygon with N sides, is:

180 * (N-2) / N

Triangle: 180 * (3-2) / 3 = 180 * 1 / 3 = 60
Square: 180 * (4-2) / 4 = 180 * 2 / 4 = 90
Pentagon: 180 * (5-2) / 5 = 540 / 5 = 108
Hexagon: 180 * (6-2) / 6 = 180 * 4 / 6 = 120

Heptagon: 180 * (7-2) / 7 = 900/7.
That's 128 + 4/7, or about 128.57 degrees.

Answer 2

Sum of exterior angle of a polygon=360 degrees
All interior angles of a regular heptagon are equal
=> All exterior angles of a regular hepatgon are equal

Each exterior angle = 360/7

Therefore each interior angle = 180-(360/7)
=128.57 degrees (approximately)