Each interior angle of a regular polygon contains 120 degrees. How many sides does the polygon have?

Answer 1

In the late 1960's, Seymour Papert and his team at M.I.T. built a computer-controlled "turtle" that could draw lines on a flat surface. You may use Logo online to draw.

A regular polygon is made by:

Turtle starting in a given position

Repeat N times

Draw a side of constant length

Turn left (the external angle amount)

End with the Turtle in the original position

Since the Turtle has turned completely around, the sum of the external angles is 360°

The internal angle is 180° - external angle,

For a regular polygon with equal internal angles of 120 °(and equal side lengths), the external angle is 60˜ (that is, 180° - 120°). The Turtle must turn left 6 times (360°/60°), so this is a regular hexagon.

Answer 2

Sketch some of the possible options:

A square? No--4 sides, and the 4 interior angles are each 90 degrees.

Next, try a pentagon (5 sides)

To get the angles in any regular polygon:

--draw a line from each vertex to the center.

--at the center you will have the same number of angles as the polygon has sides.

--to get the size of each angle divide 360 by the number of angles

--once you know the size of the center angle, find the two other angles in each triangle. The sum of the 3 must be 180 deg. so each side angle is 1/2 of (180 - the center angle)

Example: for a pentagon, the center angle is 360/5 = 72. The sum of the 2 side angles must then be 180-72 = 108, and each side angle is then 54.

Next, try a hexagon and see if it answers the problem