[b]Construct and measure[/b] the exterior angles of each of the four examples of convex polygons. [b]Record [/b]the measurements in the table provided and identify how the measures are related. You will use this relationship to [b]predict[/b] measures, [b]state[/b] the relationships, and [b]write[/b] a formula.
The GeoGebra applet in this activity lets you explore the exterior angles of four types of polygons: triangles, quadrilaterals, pentagons, and hexagons. You can construct the exterior angles by extending the sides of the polygon using the LINE tool [icon]/images/ggb/toolbar/mode_join.png[/icon]. To name the exterior angle you will have to you use the POINT tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_point.png[/icon] to identify points in the extended line. To measure the angles, use the ANGLE tool [icon]/images/ggb/toolbar/mode_angle.png[/icon]. In measuring, make sure to click the points in [b]clockwise order [/b]to get the measure of the desired angle.
What do you think would be the total number of exterior angles of a convex nonagon?
What do you think is the sum of the measurements of all the exterior angles of a convex nonagon?
How does the the number of exterior angles of a convex polygons related to its number of sides? Your answer should start with:[br][br]"The number of exterior angles of convex polygon is _________"
How does the sum of all the exterior angles of a convex polygon related to its number of sides?
If we let [i]n[/i] to be the number of sides of a polygon, what is the formula for getting the total number of exterior angles of this polygon?
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