## Polygons Exercise

1. (a) Sketch a diagram of a pentagon.

(b) Calculate the sum of the exterior angles.

(c) Calculate the sum of the interior angles.

(d) If the pentagon were regular, what would be the size of each:

(i) Exterior angle (ii) Interior angle

2. The diagram shows a regular seven-sided polygon (a heptagon).

 (a) What is the sum of the exterior angles? (b) Calculate the sum of the interior angles. (c) What is the size of each: (i) Exterior angle? (ii) Interior angle? 3. Find the sizes of the angles marked by letters.

 (a) (c) (b) (d) 4. The interior angle of a regular, n − sided polygon = (a) Find the size of an interior angle of:

(i) a square

(ii) an regular octagon

(iii) a regular dodecagon (12 sides)

(iv) an regular icosagon (20 sides)

(b) What do the answers to part (a) show about the relationship between the number of sides of a regular polygon and the size of each interior angle?

5. The exterior angles of a regular polygon are each 18°.

How many sides has the polygon?

6. The interior angles of a polygon add up to 1800°.

How many sides has the polygon? 