Find the number of sides of a regular polygon whose exterior angle and interior angle are in the ratio 1 : 5.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12
At each vertex of a polygon the exterior and interior angles lie on a straight line, so they add up to 180°. The ratio 1 : 5 therefore splits 180° into 6 parts. The exterior angles of any polygon add up to 360°, which gives the number of sides.
Exterior angle, one part of six: \(\displaystyle\frac{1}{1+5}\times180^\circ=30^\circ\)
Number of sides \(=\displaystyle\frac{360^\circ}{30^\circ}=12\)