Proof: By Euclid
(related to Corollary: Triangulation of an N-gon and Sum of Interior Angles)
- By Prop 1.32, the sum of all angles in a plane triangle is $180^\circ.$
- If a convex n-sided figure is triangulated, we will obtain \((n-2)\) triangles.
- Therefore, the sum of its angles equals \(2(n-2)\) right angles.
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References
Adapted from CC BY-SA 3.0 Sources:
- Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
- Casey, John: "The First Six Books of the Elements of Euclid"
