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Find the number of sides in a regular polygon if its each interior angle is 165°.
24
18
25
20
24
Calculate the exterior angle first using 360°/(180°−165°)=360°/15°=24.
Regular polygon with each interior angle = 165°
n=180°−θ360°
Calculate the exterior angle first using 360°/(180°−165°)=360°/15°=24.
Confusing interior angle with exterior angle; the number of sides n is calculated from the exterior angle which is (180°−interior angle).
Identify given values
The interior angle of a regular polygon is given as θ=165°.
θ=165°
Calculate exterior angle
The exterior angle of a regular polygon is 180° minus the interior angle.
Ext=180°−165°=15°
Calculate number of sides
The sum of exterior angles for any convex polygon is 360°. For a regular polygon with n sides, each exterior angle is n360°.
n=15°360°=24
A is correct because the exterior angle is 15° and 360°/15°=24 sides.
This concept is fundamental for polygon geometry questions in exams like SSC and Railway, often appearing as exterior/interior ratio problems.
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