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If each interior angle of a regular polygon is 150 degrees, then it is a/an ______________
- a)Octagon
- b)Decagon
- c)Dodecagon
- d)Tetrahedron
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If each interior angle of a regular polygon is 150 degrees, then it is...
The sum of the exterior angle and interior angle of a regular polygon is 3600.
As the measure of each interior angle is 1500, the measure of each exterior angle will be 300.
The number of sides of a regular polygon is given by the following relationship n = 360/exterior angle
As the value of each exterior angle is 300, the number of sides = 12.
As the measure of each interior angle is 1500, the measure of each exterior angle will be 300.
The number of sides of a regular polygon is given by the following relationship n = 360/exterior angle
As the value of each exterior angle is 300, the number of sides = 12.
Most Upvoted Answer
If each interior angle of a regular polygon is 150 degrees, then it is...
To determine the correct answer, we need to understand the relationship between the number of sides in a regular polygon and the measure of each interior angle.
A regular polygon is a polygon that has all sides and angles equal. The formula to calculate the measure of each interior angle of a regular polygon is given by:
Interior angle = (n-2) * 180 / n
Where n is the number of sides in the polygon.
Let's calculate the measure of each interior angle for each option:
a) Octagon (8 sides):
Interior angle = (8-2) * 180 / 8 = 6 * 180 / 8 = 135 degrees
b) Decagon (10 sides):
Interior angle = (10-2) * 180 / 10 = 8 * 180 / 10 = 144 degrees
c) Dodecagon (12 sides):
Interior angle = (12-2) * 180 / 12 = 10 * 180 / 12 = 150 degrees
d) Tetrahedron (a three-dimensional object with four triangular faces):
Tetrahedron does not have interior angles because it is not a polygon.
Therefore, the correct answer is option 'c' - Dodecagon. A regular dodecagon has 12 sides, and each interior angle measures 150 degrees.
A regular polygon is a polygon that has all sides and angles equal. The formula to calculate the measure of each interior angle of a regular polygon is given by:
Interior angle = (n-2) * 180 / n
Where n is the number of sides in the polygon.
Let's calculate the measure of each interior angle for each option:
a) Octagon (8 sides):
Interior angle = (8-2) * 180 / 8 = 6 * 180 / 8 = 135 degrees
b) Decagon (10 sides):
Interior angle = (10-2) * 180 / 10 = 8 * 180 / 10 = 144 degrees
c) Dodecagon (12 sides):
Interior angle = (12-2) * 180 / 12 = 10 * 180 / 12 = 150 degrees
d) Tetrahedron (a three-dimensional object with four triangular faces):
Tetrahedron does not have interior angles because it is not a polygon.
Therefore, the correct answer is option 'c' - Dodecagon. A regular dodecagon has 12 sides, and each interior angle measures 150 degrees.
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If each interior angle of a regular polygon is 150 degrees, then it is a/an ______________a)Octagonb)Decagonc)Dodecagond)TetrahedronCorrect answer is option 'C'. Can you explain this answer?
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If each interior angle of a regular polygon is 150 degrees, then it is a/an ______________a)Octagonb)Decagonc)Dodecagond)TetrahedronCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If each interior angle of a regular polygon is 150 degrees, then it is a/an ______________a)Octagonb)Decagonc)Dodecagond)TetrahedronCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If each interior angle of a regular polygon is 150 degrees, then it is a/an ______________a)Octagonb)Decagonc)Dodecagond)TetrahedronCorrect answer is option 'C'. Can you explain this answer?.
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