GMAT Exam > GMAT Questions > The difference between the interior and exter...
Start Learning for Free
The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?
- a)18
- b)20
- c)19
- d)15
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The difference between the interior and exterior angle at a vertex of ...
Let's assume the regular polygon has n sides.
The sum of all the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. Since the polygon is regular, all the interior angles are equal, so we can divide this sum by n to find the measure of each interior angle.
Sum of interior angles = (n-2) * 180 degrees
Each interior angle = (n-2) * 180 degrees / n
The exterior angle at each vertex of a polygon is the supplementary angle to the interior angle. So, the measure of each exterior angle is given by 180 degrees minus the measure of each interior angle.
Each exterior angle = 180 degrees - (n-2) * 180 degrees / n
The difference between the interior and exterior angle at a vertex is given to be 144 degrees.
Each interior angle - Each exterior angle = 144 degrees
[(n-2) * 180 degrees / n] - [180 degrees - (n-2) * 180 degrees / n] = 144 degrees
Now, we can solve this equation to find the value of n.
[(n-2) * 180 degrees / n] - [180 degrees - (n-2) * 180 degrees / n] = 144 degrees
Simplifying the equation:
[(n-2) * 180 degrees / n] - [180 degrees - (n-2) * 180 degrees / n] = 144 degrees
[(n-2) * 180 degrees / n] - 180 degrees + (n-2) * 180 degrees / n = 144 degrees
[(n-2) * 180 degrees / n] + (n-2) * 180 degrees / n = 324 degrees
[(n-2) * 180 degrees + (n-2) * 180 degrees] / n = 324 degrees
[(2n-4) * 180 degrees] / n = 324 degrees
Multiply both sides of the equation by n to eliminate the denominator:
(2n-4) * 180 degrees = 324 degrees * n
360n - 720 = 324n
36n = 720
n = 20
Therefore, the regular polygon has 20 sides.
The sum of all the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. Since the polygon is regular, all the interior angles are equal, so we can divide this sum by n to find the measure of each interior angle.
Sum of interior angles = (n-2) * 180 degrees
Each interior angle = (n-2) * 180 degrees / n
The exterior angle at each vertex of a polygon is the supplementary angle to the interior angle. So, the measure of each exterior angle is given by 180 degrees minus the measure of each interior angle.
Each exterior angle = 180 degrees - (n-2) * 180 degrees / n
The difference between the interior and exterior angle at a vertex is given to be 144 degrees.
Each interior angle - Each exterior angle = 144 degrees
[(n-2) * 180 degrees / n] - [180 degrees - (n-2) * 180 degrees / n] = 144 degrees
Now, we can solve this equation to find the value of n.
[(n-2) * 180 degrees / n] - [180 degrees - (n-2) * 180 degrees / n] = 144 degrees
Simplifying the equation:
[(n-2) * 180 degrees / n] - [180 degrees - (n-2) * 180 degrees / n] = 144 degrees
[(n-2) * 180 degrees / n] - 180 degrees + (n-2) * 180 degrees / n = 144 degrees
[(n-2) * 180 degrees / n] + (n-2) * 180 degrees / n = 324 degrees
[(n-2) * 180 degrees + (n-2) * 180 degrees] / n = 324 degrees
[(2n-4) * 180 degrees] / n = 324 degrees
Multiply both sides of the equation by n to eliminate the denominator:
(2n-4) * 180 degrees = 324 degrees * n
360n - 720 = 324n
36n = 720
n = 20
Therefore, the regular polygon has 20 sides.
Community Answer
The difference between the interior and exterior angle at a vertex of ...
Given:
Interior angle(I) – Exterior angle(E) = 144°
Formula used:
For any regular polygon,
Interior angle(I) + Exterior angle(E) = 180°
Each exterior angle = 360°/n, where
n = number of sides
Calculation:
ATQ,
⇒ I + E = 180° and I – E = 144°
Adding both the eq.
⇒ 2I = 324
⇒ I = 324/2 = 162°
Now, putting the value,
⇒ E = 180° – 162° = 18°
Using the formula of E,
Number of sides = 360/18° = 20
∴ The number of sides of the regular polygon is 20.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer?
Question Description
The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer?.
The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer?.
Solutions for The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The difference between the interior and exterior angle at a vertex of a regular polygon is 144°. What is the number of sides of the polygon?a)18b)20c)19d)15Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup