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If the measure of each interior angle of a regular polygon is 150°, then the number of its diagonals will be
- a)54
- b)27
- c)15
- d)12
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the measure of each interior angle of a regular polygon is 150°...
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
Community Answer
If the measure of each interior angle of a regular polygon is 150°...
To find the number of sides of a regular polygon when the measure of each interior angle is given, we can use the formula:
n = (180 * (n - 2)) / n
where n is the number of sides.
In this case, the measure of each interior angle is 150 degrees. Substituting this value into the formula, we have:
150 = (180 * (n - 2)) / n
Now, cross-multiply to get rid of the fraction:
150n = 180n - 360
Combine like terms:
180n - 150n = 360
30n = 360
Now, divide both sides by 30:
n = 12
Therefore, the regular polygon has 12 sides.
n = (180 * (n - 2)) / n
where n is the number of sides.
In this case, the measure of each interior angle is 150 degrees. Substituting this value into the formula, we have:
150 = (180 * (n - 2)) / n
Now, cross-multiply to get rid of the fraction:
150n = 180n - 360
Combine like terms:
180n - 150n = 360
30n = 360
Now, divide both sides by 30:
n = 12
Therefore, the regular polygon has 12 sides.
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If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. Can you explain this answer?
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If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. 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 If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. Can you explain this answer?.
If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. 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 If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the measure of each interior angle of a regular polygon is 150°,then the number of its diagonals will bea)54b)27c)15d)12Correct answer is option 'A'. Can you explain this answer?.
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