Sum of Exterior Angles of a Quadrilateral
Constructing the Exterior Angles of a quadrilateral
1. Using the segment tool
on the open Geogebra window below, construct a non-regular quadrilateral.
2. Label the vertices A, B, C and D using the text tool.
3. Construct one set of exterior angles using the ray tool
. 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).
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Construct the quadrilateral with exterior angles here.
4. Measure the exterior angles
. Make sure to measure the exterior angles less than 180.
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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 ___________