Sum of Exterior Angles of a Quadrilateral
Constructing the Exterior Angles of a quadrilateral
1. Using the segment tool[icon]/images/ggb/toolbar/mode_segment.png[/icon] on the open Geogebra window below, construct a non-regular quadrilateral.[br]2. Label the vertices A, B, C and D using the text tool. [icon]/images/ggb/toolbar/mode_text.png[/icon][br]3. Construct one set of exterior angles using the ray tool[icon]/images/ggb/toolbar/mode_ray.png[/icon]. Make sure your exterior angles all go the same way, like the picture below. Label the exterior parts of the angles E (next to A), F (next to B), G (by C) and H (by D).
Construct the quadrilateral with exterior angles here.
4. Measure the exterior angles [icon]/images/ggb/toolbar/mode_angle.png[/icon]. Make sure to measure the exterior angles less than 180.
5. Add your 4 angles together.
What is the sum of the 4 exterior angles?
6. Drag your vertices around and allow the angles to change. Add them again.
What is the sum of the exterior angles now?
Complete the following conjecture: The sum of the exterior angles of a quadrilateral is ___________