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If the sum of the measures of the interior angles of a polygon is
5400^(@), how many sides does the polygon have?

If the sum of the measures of the interior angles of a polygon is $5400^{\circ}$ , how many sides does the polygon have?

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Full solution

Q. If the sum of the measures of the interior angles of a polygon is

5400^{\circ}

, how many sides does the polygon have?

Calculate sum of angles: Calculate the sum of the interior angles using the formula $(n-2) \times 180$ , where $n$ is the number of sides. $\newline$ Sum of interior angles = $5400$ $\newline$ $(n-2) \times 180 = 5400$
Solve for n: Solve for n. $\newline$ $n-2 = \frac{5400}{180}$ $\newline$ $n-2 = 30$ $\newline$ $n = 32$

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