each angle of a regular polygon is 150 how many sides does it have.with steps
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Answer:
12 sides
Step-by-step explanation:
If each angle of a regular polygon measures 150°, then the polygon has 12 sides.
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Step-by-step explanation:
The answer is: 12 sides. This could be explained as following. The Polygon angle theorem states that the sum of all interior angles is equal 180(n-2), where n is the number of sides, which is also equal to the number of interior angles. Therefore, knowing the measure of of one interior angle (150 per problem definition), the sum of all interior angles could be written as 150n. Solve the following equation to find the number of sides n:
180(n-2) = 150n
n = 12
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