**Sum of Interior Angles of a Polygon Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on sum of interior angles of a polygon.

Before look at the worksheet, if you would like to know the basic stuff about sum of interior angles of a polygon,

**Problem 1 :**

Find the value of "x" in the diagram given below.

**Problem 2 :**

Find the value of "x" in the diagram given below.

**Problem 3 :**

Find the measure of each interior angle of the regular polygon given below.

**Problem 4 :**

What is the measure of each interior angle of a regular decagon ?

**Problem 5 :**

Each exterior angle of a regular polygon measures 30°. How many sides does the polygon have ?

**Problem 6 :**

Each interior angle of a regular polygon measures 160°. How many sides does the polygon have ?

**Problem 1 :**

Find the value of "x" in the diagram given below.

**Solution : **

The above diagram is an irregular polygon of 5 sides.

Formula to find the sum of interior angles of a n-sided polygon is

= (n - 2) ⋅ 180°

By using the formula, sum of the interior angles of the above polygon is

= (5 - 2) ⋅ 180°

= 3 ⋅ 180°

= 540° ------(1)

By using the angles, sum of the interior angles of the above polygon is

= 58° + 100° + 112° + 25° + x°

= 295° + x° ------(2)

From (1) and (2), we get

295° + x° = 540°

295 + x = 540

Subtract 295 from both sides.

x = 245

Hence, the value of "x" is 245.

**Problem 2 :**

Find the value of "x" in the diagram given below.

**Solution : **

The above diagram is an irregular polygon of 6 sides (Hexagon) with one of the interior angles as right angle.

Formula to find the sum of interior angles of a n-sided polygon is

= (n - 2) ⋅ 180°

By using the formula, sum of the interior angles of the above polygon is

= (6 - 2) ⋅ 180°

= 4 ⋅ 180°

= 720° ------(1)

By using the angles, sum of the interior angles of the above polygon is

= 120° + 90° + 110° + 130° + 160 + x°

= 610° + x° ------(2)

From (1) and (2), we get

610° + x° = 720°

610 + x = 720

Subtract 610 from both sides.

x = 110

Hence, the value of "x" is 110.

**Problem 3 :**

Find the measure of each interior angle of the regular polygon given below.

**Solution : **

Let us count the number of sides of the polygon given above.

So, the above regular polygon has 9 sides.

Formula to find the sum of interior angles of a n-sided polygon is

= (n - 2) ⋅ 180°

By using the formula, sum of the interior angles of the above polygon is

= (9 - 2) ⋅ 180°

= 7 ⋅ 180°

= 1260°

**Formula to find the measure of each interior angle ****of a n-sided regular ****polygon is **** **

= Sum of interior angles / n

Then, we have

= 1260° / 9

= 140°

Hence, the measure of each interior angle of the given regular polygon is 140°.

**Problem 4 :**

What is the measure of each interior angle of a regular decagon ?

**Solution : **

Decagon is a 10-sided polygon.

Formula to find the sum of interior angles of a n-sided polygon is

= (n - 2) ⋅ 180°

By using the formula, sum of the interior angles of the given decagon (10-sided polygon) is

= (8 - 2) ⋅ 180°

= 8 ⋅ 180°

= 1440°

**Formula to find the measure of each interior angle ****of a n-sided regular ****polygon is **** **

= Sum of interior angles / n

Then, we have

= 1440° / 10

= 144°

Hence, the measure of each interior angle of the given regular decagon is 144°.

**Problem 5 :**

Each exterior angle of a regular polygon measures 30°. How many sides does the polygon have ?

**Solution : **

Formula to find the number of sides of a regular polygon (when the measure of each exterior angle is known) :

= 360 / Measure of each exterior angle

Then, we have

= 360 / 30

= 12

Hence, the given polygon has 12 sides.

**Problem 6 :**

Each interior angle of a regular polygon measures 160°. How many sides does the polygon have ?

**Solution : **

In any polygon, the sum of an interior angle and its corresponding exterior angle is 180°.

That is,

Interior angle + Exterior Angle = 180°

160° + Exterior Angle = 180°

Exterior angle = 20°

So, the measure of each exterior angle is 20°.

Formula to find the number of sides of a regular polygon (when the measure of each exterior angle is known) :

= 360 / Measure of each exterior angle

Then, we have

= 360 / 20

= 18

Hence, the given polygon has 18 sides.

After having gone through problems given above, we hope that the students would have understood the stuff on, "Sum of interior angles of a polygon worksheet"

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