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?