Polygon Questions

Polygon Questions are practice problems that are given below to help the student understand the meaning of Polygon., their properties and also their characteristics that differentiate them from other shapes. By solving these problems, the student gets clarity about the topic. The polygon questions with solutions are intended to help the student give step by step solutions to the problems. Thus any confusion is sorted when the steps are referred.

What are polygons? Polygons are two dimensional geometrical figures that are formed with line segments. Since there are more than 2 line segments, a polygon has a vertex, which is the point that is obtained at the junction of line segments. There is a line segment and vertex, which results in an angle.

Polygon Rules

We will need a few formulas to solve the Polygon Questions to get solutions. Lets recap few rules

1. The sum of all the interior angles of a simple n-gon = (n − 2) × 180° or Sum = (n − 2)π radians, Where ‘n’ is equal to the number of sides of a polygon.

(This is called the Interior Angle sum property)

2. The sum of interior and the corresponding exterior angles at each vertex of any polygon are supplementary to each other.

i,e For a polygon;

Interior angle + Exterior angle = 180 degrees

(This is called the Exterior angle property)

Refer to the Polygon Definition that has more rules and formulas

Polygon Questions With Solutions

Question 1:

Give an example for a geometrical shape which is not a polygon.

Solution:

Circle is an example of a 2-D geometrical shape that is not a polygon.

Question 2:

Give 2 examples of a convex polygon.

Solution:

The two examples of a convex polygon are Pentagon and Hexagon.

Question 3:

A convex polygon has 14 diagonals find the number of sides of a polygon

Solution:

No. of diagonals in a polygon of n sides = n (n – 3 ) / 2

14 = n (n – 3) / 2

14 × 2 = n ( n – 3)

28 = n ( n – 3)

28 = 7 (7 -3)

Therefore n = 7

Question 4:

Find the sum of all the interior angles of a polygon having 13 sides.

Solution:

We know that sum of all the interior angles in a polygon = (n – 2) × 180°

Here, n = 13

Therefore, the sum of all interior angles = (13 – 2) × 180°

= 11 × 180°

= 1980°

Question 5:

The sum of all the interior angles of a polygon is 1440°. How many sides does the polygon have?

Solution:

The formula of sum of all the interior angles of a polygon is = (n – 2) × 180°

Given, the sum of interior angles of the given polygon is 1440

(n – 2) × 180 = 1440

n – 2 = 1440 / 180

n – 2 = 144 / 18 = 8

n – 2 = 8

n = 10

Question 6:

Find the exterior angle of a polygon with sides 6.

Solution:

Exterior angle = 360 / n

Given n = 6

Exterior angle = 360 / 6 = 60.

Question 7:

Is it possible to have a polygon, where the sum of whose interior angles is 9 right angles?

Solution:

To calculate the number of sides of a polygon,

Number of sides = ½ [( sum of interior angles / 90) + 4 ]

= ½ ( (9 × 90) / 90 + 4)

= ½ ( 9 + 4)

= ½ ( 13 )

= 6.5

No it is not possible to have a polygon where the sum of whose interior angles is 9 right angles, since we got the number of sides as 6.5.

Question 8:

Is it possible to have a polygon whose sum of interior angles is 910°?

Solution:

We know that

Number of sides = ½ ( sum of interior angles / 90 + 4 )

n = ½ ( 910°/90° + 4)

n = ½ (10.11 + 4 )

Since n is not a positive integer/whole number, (the value of n is in decimals), there cannot be a polygon whose interior angle is 910°.

Question 9:

Find the measure of each angle of a regular Nonagon.

Solution:

Number of sides given is 9

Formula for each interior angle is ((2n – 4) × 90) / n

= [(2 × 9 – 4) × 90] / 9

= (14 × 90) / 9

= 1260 / 9

= 140°

Question 10:

Which polygon has both its interior and exterior angles the same?

Solution:

We know that

Interior angle + Exterior angle = 180 degrees

If Interior angle = Exterior angle

Then Exterior angle + Exterior angle = 180 degrees

2 Exterior angle = 180 degrees

Exterior angle = 180 / 2

Exterior angle = 90.

But Interior angle = Exterior angle = 90 deg

Number of sides n = 360/(180 – interior angle)

n = 360 /( 180 – 90)

n = 360 / 90

n = 4.

A polygon with 4 sides has both interior angles and exterior angles as same.

Related Articles

• 2-Dshapes
• Perimeter Of Polygons
• Exterior Angles Of Polygon
• Polygon Formula

Practice Questions on Polygon

1. Calculate the sum of all interior angles of a polygon having
1. 10 side
2. 7 sides
3. 11 sides
2. Find the number of sides of a polygon the sum of whose interior angle is
   1. 540
   2. 720
3. Is it possible to have a polygon, where the sum of whose interior angles is 5 right angles?
4. Find the measure of each angle of a regular polygon.
   1. Hexagon
   2. Octagon
   3. Nonagon