FINDING NUMBER OF SIDES OF A POLYGON WORKSHEET

Problem 1 :

Each interior angle of a regular polygon is 174⁰. Find the number of sides of polygon.

Solution

Problem 2 :

The interior angle of a regular polygon is 135⁰. Work out the number of sides of the polygon.

Solution

Problem 3 :

The sum of the interior angles in a polygon is 7380⁰. Calculate the number of sides the polygon has.

Solution

Problem 4 :

Shown below is a regular pentagon ABCDE

Solution

Problem 5 :

Shown below is a regular hexagon, with an exterior angle labeled y.

Work out the size of each exterior angle.

Solution

Problem 6 :

Shown is a regular hexagon and a regular octagon.

Solution

Problem 7 :

Shown below is a regular hexagon ABCDEF.

Calculate the angle x.

Solution

Problem 1 :

The number of sides of a regular polygon where each exterior angle has a measure of 45^º is ……

a)  8        b) 10       c) 4     d) 6

Solution

Problem 2 :

a)  60^º      b) 140^º      c) 150^º     d) 108^º

Solution

Problem 3 :

If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are 

(a) 72^º, 108^º     (b) 36^º, 54^º     (c) 80^º, 120^º    (d) 96^º, 144^º

Solution

Problem 4 :

If PQRS is a parallelogram, then ∠P - ∠R is equal to

a) 60^º     b) 90^º    c) 80^º    d) 0^º

Solution

Problem 5 :

The sum of adjacent angles of a parallelogram is

a) 180^º     b) 120^º  c) 360^º  d) 90^º

Solution

Problem 6 :

The number of sides of a regular polygon whose each interior angle is of 135^º is ……

a) 6       b) 7      c) 8        d) 9

Solution

Problem 7 :

The figure given below is a regular pentagon, find the value of x.

Solution

Problem 8 :

A polygon has an interior angle that is five times larger than the exterior angle. How many sides does it have?

Solution

Problem 9 :

The diagram shows three regular pentagons meeting at a point. Work out the size of the angle marked x. You must show all your working.

Solution

Problem 10 :

The diagram shows regular 5 sided polygon with center O.

Solution

Problem 11 :

Shape A is a regular triangle. Shape B is a regular octagon.

Another regular polygon, P, is shown on the diagram.

How many sides does polygon P have? You must show your working.

Solution

Problem 1 :

For the following regular polygon given below,

find

(i)  Number of sides that the polygon has

(ii) Number of angles

(iii)  Size of each angle.

Solution

Problem 2 :

Find the size of each angle of a regular 12 sided polygon.

Solution

Problem 3 :

Each exterior angle of a regular polygon is 20⁰. Work out the number of sides of the polygon.

Solution

Problem 4 :

The trampoline shown is shaped like a regular dodecagon

a. Find the measure of each interior angle.

b. Find the measure of each exterior angle.

Solution

Problem 5 :

The floor of the gazebo shown is shaped like a regular decagon. Find the measure of each exterior angle of the regular decagon. Find the measure of each exterior angle.

Solution

Problem 6 :

Write a formula to find the number of sides n in a regular polygon given that the measure of one interior angle is x°.

Solution

Problem 7 :

Write a formula to find the number of sides n in a regular polygon given that the measure of one exterior angle is x°.

Solution

Problem 8 :

Which of the following angle measures are possible interior angle measures of a regular polygon? Explain your reasoning. Select all that apply.

a) 162°     b) 171°    c) 75°     d) 40°

Solution