# What is the measure of one interior angle of a regular 15 sided polygon?

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Number the vertices with consecutive integers 1 through 15. Let the edge (side) of the polygon connecting vertex i and vertex i+1 be called edge

Since the polygon is regular, all sides and angles are equal, so each turn at each vertex is the same, and of size

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In any convex polygon, if you start at one vertex and draw the diagonals to all the other vertices, you will form triangles,

The number of triangles so formed is always

For an

The sum of the interior angles is therefore

In a

Sum interior angles =

Each interior angle of the regular polygon =

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