Draw three different nonconvex polygons. When you walk
around a polygon, at each vertex you need to turn either
right (clockwise) or left (counterclockwise). A turn to the
left is measured by a positive number of degrees and a turn
to the right by a negative number of degrees. Find the sum
of the measures of the turn angles of the polygons you
drew. Assume you start at a vertex facing in the direction
of a side, walk around the polygon, and end up at the same
vertex facing in the same direction as when you started.
There is a theorem about the sum of the external angles of a polygon. Check it out.
http://www.mathwarehouse.com/geometry/polygon/index.php
THANKS!!!!! That website was great!
To find the sum of the measures of the turn angles of the polygons you drew, we need to determine the degree measure of each turn at the vertices of the polygons. Here's how you can do that:
1. Start by drawing a nonconvex polygon. One example is a triangle with two acute angles and one obtuse angle. Label the vertices A, B, and C in a counterclockwise direction.
2. To find the degree measure of the turn at vertex A, measure the angle formed by the line segments AB and AC. Note that since we are walking counterclockwise around the polygon, turning left at A means the angle measure will be positive. Let's say the measure of angle BAC is 60 degrees. This means a turn to the left at A measures +60 degrees.
3. Repeat this process for the other vertices of the polygon. At vertex B, measure the angle formed by BC and BA. Let's say the measure of angle CBA is 90 degrees. Since we are turning left at B in a counterclockwise direction, the measure of the turn at B is +90 degrees.
4. Finally, measure the angle formed by AC and BC at vertex C. Let's say the measure of angle ACB is 120 degrees. Since we are turning left at C in a counterclockwise direction, the degree measure of the turn at C is +120 degrees.
5. Now, add up the degree measures of all the turns in the polygon. In this example, +60 degrees at A, +90 degrees at B, and +120 degrees at C. The sum of the measures of the turn angles in this polygon is 60 + 90 + 120 = 270 degrees.
6. Repeat this process to draw two more nonconvex polygons of your choice. Measure the degree measures of the turns at each vertex and calculate their sum using the same approach outlined above.
By following these steps, you can find the sum of the measures of the turn angles for any nonconvex polygon you draw.