Use the geometry software to construct a polygon with five s

Use the geometry software to construct a polygon with five sides. Then, beginning at one vertex and continuing clockwise, extend each side of the polygon to form one exterior angle at each vertex as in the figure below Example: Measure each exterior angle, and determine the sum of the measures. Using the drag feature, grab one vertex and move it around to alter the figure. Observe any changes in the measure of each exterior angle and the sum of the measures of the exterior angles. Record the measure of each exterior angle and the sum of the measures of the exterior angles for one polygon in the table. Repeat the process for polygons with 6, 7,8, and 9 sides. Measure of Each Exterior Angle Polygon Sum 1 2 3 4 5 6 7 89 5 sides 6 sides 7 sides 8 sides 9 sides What can you conclude about the sum of the measures of the exterior angles of a convex polygon? Explain. I.

Solution

Lets get some basicunderstanding of polygons:

A regular polygon is one where all the sides are equal.

1) The sum of the interior angles of a polygon is given by (2n-4)*90, where n is the number of sides.

eg if n = 3 (a triangle) then sum of the interior angles = (2*3 - 4) * 90 = 180

2) Each interior angle of a regular polygon is therefore (2n-4)*90/n..so for an equilateral triangle, each interior angle is 180/3 = 60

3) Now the sum of exterior angles of a polygon is = 360 (this is standard for all polygons) and

4) Any interior angle + its exterior angle = 180 (since they both lie on a straight line and sum of angles on a straight line = 180

So coming back to the question, the sum of the exterior angles of a polygon = 360. Therefore each exterior angle = 360/n

So for a 5 sided figure, each exterior angle = 360/5 = 72

For a 6 sided polygon, each exterior angle = 360/6 = 60

For a 7 sided polygon, each exterior angle = 360/7 = 51.4286

For a 8 sided polygon, each exterior angle = 360/8 = 45

For a 9 sided polygon, each exterior angle = 360/9 = 40

so the answer to q1 is that sum of exterior angles is always 360.

Hope this helps