INTERIOR ANGLES OF A REGULAR POLYGON WORKSHEET

Problem 1 :

Solve for x.

Solution

Problem 2 :

Solve for x.

Solution

Problem 3 :

Solve for x.

Solution

Problem 4 :

The sum of the angles of a polygon is 1980°. How many angles has the polygon?

Solution

Problem 5 :

Juan claims to have found a polygon which has angles with a sum of 2500°. Comment on Juan’s finding.

Solution

Problem 6 :

An exterior angle and the interior angle of a regular polygon are in the ratio 2 : 7. Find the number of sides of a polygon.

Solution

Problem 7 :

Four angles of a quadrilateral are in the ratio of 3 : 4 : 5 : 6. Find its angles.

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Solution

Problem 11 :

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Problem 1 :

Find the number of sides of a regular polygon which has angles of 150°

Solution

Problem 2 :

Is there a regular polygon which has the angle of 158°

Solution

Problem 3 :

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 4 :

In an equilateral hexagon, four of the exterior angles each have a measure of x°. The other two exterior angles each have a measure of twice the sum of x and 48. Find the measure of each exterior angle.

Solution

Problem 5 :

Is the hexagon a regular hexagon. Explain your reasoning.

Solution

Problem 6 :

Describe and correct the error in finding the measure of one exterior angle of a regular pentagon.

Problem 7 :

Find the number of sides for the regular polygon described.

Each interior angle has a measure of 156°.

Solution

Problem 8 :

A home plate for a baseball field is shown.

a. Is the polygon regular? Explain your reasoning.

b. Find the measures of ∠C and ∠E.

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