In a regular polygon, the ratio of each interior angle to each exterior angle is \(7:2\). How many sides does the polygon have?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9
At each vertex the interior and exterior angles together make \(180^\circ\), and the exterior angles of any polygon add up to \(360^\circ\).
Interior \(:\) exterior \(=7:2\), so the exterior angle is \(\displaystyle\frac{2}{7+2}\times180^\circ=40^\circ\)
Interior angle \(=180^\circ-40^\circ=140^\circ\) (check: \(140:40=7:2\))
Number of sides \(\displaystyle=\frac{360^\circ}{40^\circ}=9\)
