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Problem of the Week
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.

Triangle AOB with dashed lines for sides OA and OB and a solid line for side AB. Angles OAB measures 20 degrees.

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.

Five triangles with the same size and shape as AOB share vertex O and form a figure that looks similar to five side by side triangular slices of a pie with centre O. The outer edge of the pie is made up of straight line segments, each the same length as AB. For each triangular slice, the angle at centre O measures 20 degrees. An arrow indicates that more triangles can be added to the figure.

  1. How many sides does Priya’s completed polygon have?

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

Theme: Geometry