Polygon MCQ Quiz - Objective Question with Answer for Polygon - Download Free PDF
Last updated on Apr 26, 2025
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?
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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:
Answer (Detailed Solution Below)
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
∴ A 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 ________.
Answer (Detailed Solution Below)
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 ________.
Answer (Detailed Solution Below)
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:
Answer (Detailed Solution Below)
Polygon Question 6 Detailed Solution
Download Solution PDFConcept:
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.
Answer (Detailed Solution Below)
Polygon Question 7 Detailed Solution
Download Solution PDFGiven:
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:
Answer (Detailed Solution Below)
Polygon Question 8 Detailed Solution
Download Solution PDFEach 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°?
Answer (Detailed Solution Below)
Polygon Question 9 Detailed Solution
Download Solution PDFGiven:
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
Answer (Detailed Solution Below)
Polygon Question 10 Detailed Solution
Download Solution PDFConcept:
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.
Answer (Detailed Solution Below)
Polygon Question 11 Detailed Solution
Download Solution PDFGiven
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.
Answer (Detailed Solution Below)
Polygon Question 12 Detailed Solution
Download Solution PDFEach 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?
Answer (Detailed Solution Below)
Polygon Question 13 Detailed Solution
Download Solution PDFGiven:
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:
Answer (Detailed Solution Below)
Polygon Question 14 Detailed Solution
Download Solution PDFGiven:
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 polygonCalculation:
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:
Answer (Detailed Solution Below)
Polygon Question 15 Detailed Solution
Download Solution PDF⇒ Number of diagonal in a n-gon = {n(n – 3)}/2
⇒ Number of diagonal in a 26-gon = {26(26 – 3)}/2 = 299