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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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