Sum of Exterior Angles of a Triangle
Constructing the Exterior Angles of a triangle
1. On the open Geogebra window below, use the segment tool
to construct a non-regular triangle.
2. Label the vertices A, B and C 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 D (next to A), E (next to B) and F (by C).
![Toolbar Image](/images/ggb/toolbar/mode_segment.png)
![Toolbar Image](/images/ggb/toolbar/mode_text.png)
![Toolbar Image](/images/ggb/toolbar/mode_ray.png)
![Image](https://www.geogebra.org/resource/YcF8weVW/Sj4yv5FYc35WP6Ku/material-YcF8weVW.png)
Construct the triangle and exterior angles below.
4. Measure angles DAB, EBC and FCA
. Select either the two lines that make the angle or 3 vertices to measure the angle. Make sure to measure the exterior angles less than 180.
![Toolbar Image](/images/ggb/toolbar/mode_angle.png)
![Image](https://www.geogebra.org/resource/AW9zTkxg/xsctVbRc1jlhD0ch/material-AW9zTkxg.png)
5. Add your 3 angles together.
What is the sum of the 3 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 triangle is ___________