Problem C

One Dot at a Time

Priya is drawing a polygon on a piece of wood. First she hammers a nail into the piece of wood, calling this point \(O\). Then she attaches one end of a piece of string to the nail, and the other end to a pencil. She pulls the string tight and makes a dot on the wood, calling this point \(A\). Keeping the string tight, she rotates it \(20^\circ\) clockwise and makes another dot, calling this point \(B\). She then connects points \(A\) and \(B\) with a straight line.

She repeats this process, rotating the string \(20^\circ\) clockwise, making a dot, and connecting this point to the previous point with a straight line each time, until she has gone all the way around the circle and completed the polygon.

How many sides does Priya’s completed polygon have?

What is the sum of all the interior angles in the polygon?

**Theme:** Geometry