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If the sum of interior angles of a polygon is 540 degrees, how many sides does it have?
4
5
6
7
5
Divide the sum by 180 and add 2. Since 540 / 180 = 3, then 3 + 2 = 5.
Sum of interior angles of a polygon S = 540 degrees.
S=(nтИТ2)├Ч180┬░
Divide the sum by 180 and add 2. Since 540 / 180 = 3, then 3 + 2 = 5.
Students often confuse the sum of interior angles with the sum of exterior angles, which is always 360 degrees for any convex polygon.
Identify the formula
The sum of the interior angles of a polygon with n sides is given by the formula (nтИТ2)├Ч180┬░.
S=(nтИТ2)├Ч180┬░
Substitute known values
Substitute the given sum 540┬░ into the equation: 540=(nтИТ2)├Ч180.
540=(nтИТ2)├Ч180
Solve for n
Divide both sides by 180 to get nтИТ2=3. Then add 2 to both sides to find n=5.
n=180540тАЛ+2=3+2=5
B is correct because solving the equation (nтИТ2)├Ч180=540 results in n=5, which identifies the polygon as a pentagon.
Remember that for any polygon, the sum of exterior angles is always 360┬░, which is a useful constant when solving problems involving regular polygons.
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