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Sum of Exterior Angles of a Quadrilateral

Constructing the Exterior Angles of a quadrilateral

1. Using the segment toolToolbar Image on the open Geogebra window below, construct a non-regular quadrilateral. 2. Label the vertices A, B, C and D using the text tool. Toolbar Image 3. Construct one set of exterior angles using the ray toolToolbar Image. 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 Toolbar Image. 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 ___________