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The interior angles of a regular polygon sum up to 1080 degrees. How many sides does the polygon have?
6
7
8
9
8
Divide the total sum by 180 directly to get n−2, then add 2 to find the number of sides n quickly.
Sum of interior angles of a regular polygon = 1080 degrees
Sum=(n−2)×180°
Divide the total sum by 180 directly to get n−2, then add 2 to find the number of sides n quickly.
Confusing interior angle sum formula (n−2)×180° with exterior angle sum which is always 360°.
State the Formula
The sum of all interior angles of a polygon with n sides is given by the standard formula: Sum=(n−2)×180°
Sum=(n−2)×180°
Substitute the Given Value
Substitute the given sum of interior angles (1080°) into the formula: 1080°=(n−2)×180°
1080°=(n−2)×180°
Solve for n
Divide both sides by 180° to find n−2: 1801080=n−2⟹6=n−2
6=n−2
Calculate Final Sides
Add 2 to both sides to solve for n: n=6+2=8
n=8
C is correct because the calculated number of sides for the regular polygon is 8.
This concept frequently combines with exterior angle properties and finding the measure of each individual interior angle in railway and competitive exams.
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