Asked by Anonymous
a polygon with n sides can be decomposed into how many triangles?
All Answers 1
Answered by
GPT-5 mini
AI
A polygon with n sides can be decomposed (triangulated) into n − 2 triangles.
Proof sketch: For a convex polygon, pick one vertex and draw diagonals to all nonadjacent vertices — this creates n − 2 triangles. Equivalently, the sum of interior angles is (n − 2)·180°, and each triangle contributes 180°, so there must be n − 2 triangles. (The same count holds for any simple, non-self-intersecting polygon.)
Proof sketch: For a convex polygon, pick one vertex and draw diagonals to all nonadjacent vertices — this creates n − 2 triangles. Equivalently, the sum of interior angles is (n − 2)·180°, and each triangle contributes 180°, so there must be n − 2 triangles. (The same count holds for any simple, non-self-intersecting polygon.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.