Polygon MCQ Quiz - Objective Question with Answer for Polygon - Download Free PDF

Last updated on Apr 26, 2025

Exams like SSC CGL, GD, MTS etc commonly feature Mensuration in their syllabus. One of the most important parts of Mensuration is Polygon. Candidates must prepare Polygon MCQs Quiz effectively as they can be quite confusing at times. Testbook has curated these questions for candidates to prepare Polygon objective questions well. This article also lists down a few tips and shortcuts to solve Polynomial questions quickly with accuracy. Check out these Polynomial question answers and practice these problems with Testbook now!

Latest Polygon MCQ Objective Questions

Polygon Question 1:

If a regular polygon has 10 sides, then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

  1. 120
  2. 132
  3. 108
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 108

Polygon Question 1 Detailed Solution

Concept used:

If the number of sides of a regular polygon be n, then

The interior angle = \( \frac{(n - 2) \times 180^\circ }{n}\)

Calculation:

Let the required difference be x.

No. of sides of a regular polygon = 10

According to the question

\(\Rightarrow \frac{{\left( {n - 2} \right) \times 180^\circ }}{n} - \frac{{360^\circ }}{n} = x\)

\(\Rightarrow \frac{{\left( {10 - 2} \right) \times 180^\circ }}{{10}} - \frac{{360^\circ }}{{10}} = x\)

\(\Rightarrow \frac{{8 \times 180^\circ }}{{10}} - 36^\circ = x\)

⇒ 144 - 36° = x

∴ x = 108°

Polygon Question 2:

Find the ratio of the measure of the angle of a regular pentagon to the measure of the angle of a regular octagon.

  1. 7 : 8
  2. 5 : 6
  3. 4 : 5
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 4 : 5

Polygon Question 2 Detailed Solution

Given:

A regular pentagon has 5 sides, and a regular octagon has 8 sides.

The measure of the interior angle of a regular polygon is given by:

Interior angle = [(n - 2) × 180] / n, where n is the number of sides.

Formula used:

Ratio = Measure of the angle of the pentagon / Measure of the angle of the octagon

Calculations:

Step 1: Calculate the measure of the angle of the pentagon:

Angle = [(5 - 2) × 180] / 5

Angle = (3 × 180) / 5

Angle = 540 / 5

Angle = 108°

Step 2: Calculate the measure of the angle of the octagon:

Angle = [(8 - 2) × 180] / 8

Angle = (6 × 180) / 8

Angle = 1080 / 8

Angle = 135°

Step 3: Find the ratio:

Ratio = 108 / 135

Ratio = 4 / 5

The ratio of the measure of the angle of a regular pentagon to the measure of the angle of a regular octagon is 4:5.

Polygon Question 3:

The number of diagonals in a pentadecagon is:

  1. 60
  2. 90
  3. 30
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 2 : 90

Polygon Question 3 Detailed Solution

Concept used:

1. A pentadecagon has 15 sides.

2. Number of diagonals of a polygon = n(n - 3)/2 (where n = no. of sides of the polygon)

Calculation:

Now, the number of diagonals of the pentadecagon

⇒ 15(15 - 3) ÷ 2

⇒ 90

∴ pentadecagon has 90 diagonals.

Polygon Question 4:

Each internal angle of a regular polygon exceeds each internal angle of another regular polygon by 18°. If the second polygon has half the number of sides as the first, then the number of sides in the first polygon is ________.

  1. 10
  2. 20
  3. 15
  4. More than one of the above
  5. None of the above

Answer (Detailed Solution Below)

Option 2 : 20

Polygon Question 4 Detailed Solution

Formula used:

Each Interior Angles = \(\rm\frac{n−2}{n}\) x 180° 

Calculation:

Let the number of sides of the polygons be 2n and n respectively.

According to the question:

18 = \(\rm\frac{2n−2}{2n}\) × 180° − \(\rm\frac{n−2}{n}\) × 180° 

18 = \(\rm\left[\frac{n−1}{n}−\frac{n−2}{n}\right]\) 180°

18 = \(\rm\frac{1}{n}\) × 180°

⇒ n = 10

∴ 2n = 20

Polygon Question 5:

If the number of diagonals in regular polygon is 44, then the number of sides in the polygon will be ________.

  1. 12
  2. 9
  3. 10
  4. 11

Answer (Detailed Solution Below)

Option 4 : 11

Polygon Question 5 Detailed Solution

Given:

The number of diagonals in a regular polygon = 44

Formula used:

The number of diagonals in a polygon with n sides is given by:

\(\dfrac{n(n-3)}{2} = 44\)

Calculation:

\(\dfrac{n(n-3)}{2} = 44\)

\(n(n-3) = 88\)

\(n^2 - 3n - 88 = 0\)

⇒ \(n^2 - 11n + 8n - 88 = 0\)

⇒ n(n - 11) + 8(n - 11) = 0

⇒ (n - 11) (n + 8) = 0

⇒ n = 11 and - 8

Considering the positive value:

⇒ n = 11.

∴ The correct answer is option (4).

Top Polygon MCQ Objective Questions

The ratio of the measures of each interior angle of a regular octagon to that of the regular dodecagon is:

  1. 8 : 12
  2. 9 : 10
  3. 12 : 8
  4. 4 : 5

Answer (Detailed Solution Below)

Option 2 : 9 : 10

Polygon Question 6 Detailed Solution

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Concept:

Octagon has eight sides.

Dodecagon has twelve sides.

Formula:

Interior angle of polygon = [(n – 2) × 180°] /n

Calculation:

Interior angle of octagon = [(8 – 2)/8] × 180° = 1080°/8 = 135°

Interior angle of dodecagon = [(12 – 2)/12] × 180° = 1800°/12 = 150°

∴ The ratio of the measures of the interior angles for octagon and dodecagon is 9 : 10

If the external angle of a polygon is 45° then find the number of diagonal in this polygon.

  1. 20
  2. 40
  3. 15
  4. 30

Answer (Detailed Solution Below)

Option 1 : 20

Polygon Question 7 Detailed Solution

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Given:

External angle = 45° 

Formula used:

External angle = (360°/n)

Number of diagonal of a n side polygon = (n2 - 3n)/2

Where, n = Equal to the number of side of a polygon

Calculation:

External angle = (360°/n)

⇒ 45° = (360°/n)

⇒ n = 8 

Now, Number of diagonal of a 'n' side polygon

⇒ (n2 - 3n)/2

⇒ (64 - 24)/2

⇒ 20

∴ The number of diagonal is 20.

The number of sides of a regular polygon whose interior angles are each 150° is:

  1. 15
  2. 13
  3. 12
  4. 14

Answer (Detailed Solution Below)

Option 3 : 12

Polygon Question 8 Detailed Solution

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Each interior angle is 150

Exterior angle = 180 - 150 = 30

We know,

Exterior angle = 360°/Number of sides

⇒ Number of sides = 360°/Exterior angle = 360/30 = 12

Find the number of sides of a polygon whose sum of all interior angle is 2160°?

  1. 15
  2. 14
  3. 12
  4. 13

Answer (Detailed Solution Below)

Option 2 : 14

Polygon Question 9 Detailed Solution

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Given:

Sum of all interior angles = 2160° 

Formula used:

Sum of interior angles of polygon = (n - 2) × 180° 

Where 'n' is the number of sides of the polygon.

Calculation:

∵ The sum of all the angles of the polygon = 2160° 

⇒ (n - 2) × 180° = 2160° 

⇒ n - 2 = 2160°/180° 

⇒ n - 2 = 12

⇒ n = 12 + 2

⇒ n = 14

If the measure of each interior angle of a regular polygon is 150°, then the number of its diagonals will be

  1. 54
  2. 27
  3. 15
  4. 12

Answer (Detailed Solution Below)

Option 1 : 54

Polygon Question 10 Detailed Solution

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Concept:

Each angle of n-sided polygon = ((n - 2) × 180)/n

Number of diagonals of n - sided polygon = n(n - 3)/2

Calculation:

Each interior angle = 150° 

150° = (n - 2) × 180)/n

⇒ 6n - 12 = 5n

n = 12 = Total side of the polygon

∴ Number of diagonals of n - sided polygon = n(n - 3)/2 = 108/2

∴ Number of diagonals of n - sided polygon = 54

If one of the internal angle of a regular polygon is 135°, Then find the number of diagonals in the polygon.

  1. 16
  2. 18
  3. 20
  4. 24

Answer (Detailed Solution Below)

Option 3 : 20

Polygon Question 11 Detailed Solution

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Given

One of the internal angles of a regular polygon is 135°

Concept

Each interior angle of a regular polygon = [(n -2)/n] × 180° 

Number of diagonals = [n(n - 3)/2] 

Calculation

⇒ 135° = [(n -2)/n] × 180°  

⇒ (135°/180°) = [(n -2)/n]

⇒ (3/4) = [(n -2)/n]

⇒ 3n = 4n - 8

⇒ n = 8

Now, we get

⇒ Number of diagonals = 8(8 - 3)/2

⇒ Number of diagonals = 20 

∴ Number of diagonals is 20

If each interior angle of a regular polygon is 135°, then find the number of diagonals of the polygon.

  1. 12
  2. 14
  3. 16
  4. 20

Answer (Detailed Solution Below)

Option 4 : 20

Polygon Question 12 Detailed Solution

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Each interior angle of a regular polygon is 135,

⇒ Exterior angle = 180° - Interior angle = 45°

⇒ Number of sides of polygon = 360°/Exterior angle = 8

∴ Number of diagonals = n(n - 3)/2 = 8 × (8 - 3)/2 = 20, where n is the number of sides of a polygon.

If the sum of interior angles of a polygon is 1080°, what is the number of diagonals in it?

  1. 18
  2. 20
  3. 16
  4. 15

Answer (Detailed Solution Below)

Option 2 : 20

Polygon Question 13 Detailed Solution

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Given:

The sum of interior angles of a polygon = 1080°

Formula used:

The sum of interior angles of a polygon = (n – 2)180°

Number of diagonals = [n(n – 3)]/2

Here,

n = number of sides

Calculation:

The sum of interior angles of a polygon = 1080°

⇒ (n – 2)180° = 1080°

⇒ n – 2 = 6

⇒ n = 8

⇒ Number of diagonals = [n(n – 3)]/2

⇒ Number of diagonals = (8 × 5)/2 = 20

∴ Required answer is 20.

Find the measure of each interior angle of a regular polygon of 15 sides:

  1. 106° 
  2. 156°
  3. 206°
  4. 256°

Answer (Detailed Solution Below)

Option 2 : 156°

Polygon Question 14 Detailed Solution

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Given:

Regular polygon with 15 sides

Formula Used:

The sum of interior angles of polygon of n sides

= (n − 2) × 180° where  is the number of sides of polygon

Calculation:

The sum of interior angles of polygon of 15 sides

(15 − 2) × 180° = 2340°

∴ Each interior angle  2340/15 = 156° 

The number of diagonals in a 26-gon is:

  1. 300
  2. 325
  3. 299
  4. 650

Answer (Detailed Solution Below)

Option 3 : 299

Polygon Question 15 Detailed Solution

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⇒ Number of diagonal in a n-gon = {n(n – 3)}/2

⇒ Number of diagonal in a 26-gon = {26(26 – 3)}/2 = 299
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