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Using the same methods as for hexagons to the right (i'll let you do the pictures) to find the sum of the interior angles of a nonagon, divide it up into triangles there are seven triangles because the sum of the angles of each triangle is 180 degrees we get. so, the sum of the interior angles of a nonagon is 1260 degrees. One way to find the sum of the interior angles of a polygon is to divide the polygon into triangles. choose one vertex, or corner, of the polygon and draw straight lines joining this vertex to all. Sum of interior angles = 360 ° how to find one interior angle. to find the measure of a single interior angle, then, you simply take that total for all the angles and divide it by n, the number of sides or angles in the regular polygon. the new formula looks very much like the old formula:. An interior angle is an angle inside a shape. example: pentagon. a pentagon has 5 sides, and can be made from three triangles, so you know what.. its interior angles add up to 3 × ...