MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures
Problem
A polygon has n sides (n≥3). One vertex is chosen, and all possible diagonals from that vertex are drawn, dividing the polygon into triangles.
(i) How many triangles are formed? Express your answer in terms of n and justify it.
(ii) Using the result of part (i) and the angle-sum property of a triangle, derive a general formula for the sum of the interior angles of the n-sided polygon.
(iii) Apply your formula to find the sum of the interior angles of a regular decagon.