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!

Option 1 : 54

**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

Option 2 : 9 : 10

**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**

Option 2 : 15

**Formula used :**

External angle = 180° - internal angle

Number of sides of polygon = 360/(external angle)

**Calculation :**

Internal angle = 156°

⇒ External angle = 180° - 156°

⇒ External angle = 24°

⇒ Number of sides of regular polygon = 360°/24°

⇒ Number of sides of regular polygon = 15

**∴ The number of sides of the regular polygon is 15.**

Option 4 : 540°

We know that,

Sum of all the interior angles of a polygon = (n – 2)π, where n is the number of side in the polygon.

In pentagon, n = 5

⇒ Sum of all the interior angles of a pentagon = (5 – 2)π = 3 × 180°

= 540°Option 4 : 4 : 9

**Formula:**

Each exterior angle of the polygon = 180° - Each interior angle of the polygon

Each exterior angle of the polygon = 360°/(Number of sides)

**Calculation:**

Each exterior angle of the regular hexagon = 360°/6 = 60°

Each exterior angle of the regular octagon = 360°/8 = 45°

Each interior angle of the regular octagon = 180° - 45° = 135°

∴ Required ratio = 60° : 135° = 4 : 9Option 2 : 14

**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

Option 2 : 40

For a regular polygon the number of sides is equal to 360°/exterior angle.

⇒ 360°/9° = 40

Number of sides = 40

Option 3 : 120°

**GIVEN:**

Number of sides of polygon = 12

**FORMULA USED:**

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

Exterior angle of polygon of n sides = 360/n

**CALCULATION:**

Interior angle of polygon of 12 sides = [(n – 2) × 180]/n

⇒ [(12 – 2) × 180]/12

⇒ 10 × 15

⇒ 150°

Exterior angle of polygon of 12 sides = 360/n

⇒ 360/12 = 30°

∴ required difference = 150 – 30 = 120°

Option 3 : 60°

**GIVEN:**

In a regular hexagon ABCDEF, AB and DC, when extended meet at a point P outside of hexagon

**CONCEPT USED:**

Each interior angle of a polygon = [(n – 2) × 180°]/n, where, n is the number of sides.

**CALCULATION:**

According to question –

Each interior angle of a polygon = (6 – 2) × 180°/6 = 120°

So, ∠ABC = ∠BCD = 120°

∴ ∠CBP = ∠BCP = 60°

Therefore, in ΔCBP –

⇒ 60° + 60° + ∠BPC = 180°

⇒ 120° + ∠BPC = 180°

⇒ ∠BPC = 60°

Option 3 : 26

**Given:**

The sum of all interior angle of a polygon is 4320°

**Concept used:**

The sum of all interior angle of polygon = (n - 2) × 180°

Where, n = number of sides in a polygon

**Calculation:**

The sum of all interior angle of a polygon is 4320°

**∴** 4320° = (n - 2) × 180°

⇒ n = 26

Option 3 : Rs. 4440

The area of a regular hexagon = (3√3/2).side^{2}

According to the question,

⇒ 2400√3 = (3√3/2).side^{2}

⇒ side = 40 m.

Perimeter of hexagonal field = 6 × side = 6 × 40 = 240 m

Cost of fencing = 18.50 × 240 = Rs.4440Option 3 : 299

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

⇒ Number of diagonal in a 26-gon = {26(26 – 3)}/2 = 299Option 4 : 900°

As we know,

Sum of the interior angles of a regular polygon of side n = (n – 2) × 180

Sum of the interior angles of a regular heptagon (seven-side polygon) = 5 × 180 = 900°Option 2 : 156°

**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°

Option 1 : 140°

**Given:**

Five angles of a hexagon measure 116° each.

**Formula used:**

Total angle of any regular polygon = (n - 2)× 180

**Calculation:**

Sum of internal angles in a hexagon(n = 6)

⇒ (6 - 2)× 180

⇒ 720^{o}

According to the question,

Five angles is 116° × 5 = 580°

Remaining angle = 720° - 580°

⇒ 140°

**∴ The measure of the remaining angle is 140 ^{o}**.

Option 3 : 8

**Given- **

The interior angle of a regular polygon exceeds its exterior angle by 90°

**Concept Used-**

Sum of interior angle and exterior angle of a regular polygon = 180°

Exterior angle of a regular polygon = 360/n [where n = number of sides]

**Calculation-**

Let the exterior angle of polygon be x and number of sides of polygon be n

According to Condition-

x + x + 90° = 180°

⇒ x = 45°

Now,

45 = 360/n

⇒ n = 8

∴ The number of sides of the polygon is 8.

Option 1 : 3√11 – 7

From the figure we can write;

a^{2} = (6 – a)^{2}/4 + (8 – a)^{2}/4

a^{2} = 9 + a^{2}/4 – 3a + 16 + a^{2}/4 – 4a

a^{2 }= a^{2}/2 – 7a + 25

a^{2}/2 + 7a – 25 = 0

a^{2} + 14a – 50 = 0

∴ Side of the octagon = [3√11 – 7] cm

**Note∶ This is a question of SSC CGL 2017 (Tier II) conducted on 17 Feb 2018. The question is technically incorrect. However, the solution has been provided accordingly.**

Option 3 : 144

∴ Interior angle of a regular polygon whose side is n = (n - 2)/n × 180° = (10 - 2)/10 × 180 = 144°

Option 4 : 20

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.Option 4 : 35

Number of diagonal of a polygon = [n × (n – 3)] /2

For decagon, n = 10

∴ Number of diagonals = (10 × 7)/ 2 = 35