Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Find each interior angle of a regular octagon in radians. Then find the number of sides of a regular polygon whose interior angle is rad.
One radian is the angle at the centre of a circle when the arc is as long as the radius, so . A full turn is rad, and rad . Degrees into radians: multiply by . Radians into degrees: multiply by . The interior angles of a polygon with sides add up to .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The octagon. rad.
Step 2. The exterior angle. An interior angle of leaves an exterior angle of .
Step 3. The sides. The exterior angles add up to , so .
Answer: rad; sides.
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