. If the sum of all interior angles of a polygon is 16 right angles, then find the number of sides of the polygon.
Question
If the sum of all interior angles of a polygon is 16 right angles, then find the number of sides of the polygon.
Solution
Sure, here is the step by step solution:
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We know that the sum of all interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon.
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In this case, the sum of all interior angles is given as 16 right angles. We know that 1 right angle is equal to 90 degrees. So, 16 right angles is equal to 16 * 90 = 1440 degrees.
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Substituting the given sum of interior angles into the formula, we get:
(n-2) * 180 = 1440
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Simplifying this equation, we get:
n - 2 = 1440 / 180
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Solving for n, we get:
n = 1440 / 180 + 2
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Therefore, the number of sides of the polygon is n = 8.
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