JAMB - Mathematics (2023 - No. 6)
The interior angle of a regular polygon is five times the size of its exterior angle. Identify the polygon.
dodecagon
enneadecagon
icosagon
hendecagon
Explication
An interior angle of a regular polygon = \(\frac{(2n-4)\times 90}{n}\)
An exterior angle of a regular polygon = \(\frac{360}{n}\)
\(\frac{(2n-4)\times 90}{n}\) =5 \(\times\) \(\frac{360}{n}\) (Given)
= (2n-4) x 90 = 5 x 360
= 180n - 360 = 1800
= 180n = 1800 + 360
= 180n = 2160
= n = \(\frac{2160}{180}\) = 12
The polygon has 12 sides which is dodecagon
An exterior angle of a regular polygon = \(\frac{360}{n}\)
\(\frac{(2n-4)\times 90}{n}\) =5 \(\times\) \(\frac{360}{n}\) (Given)
= (2n-4) x 90 = 5 x 360
= 180n - 360 = 1800
= 180n = 1800 + 360
= 180n = 2160
= n = \(\frac{2160}{180}\) = 12
The polygon has 12 sides which is dodecagon