The interior angle of a regular polygon is five times the size of its exterior...
MATHEMATICS
JAMB 2023
The interior angle of a regular polygon is five times the size of its exterior angle. Identify the polygon.
- A. dodecagon
- B. enneadecagon
- C. icosagon
- D. hendecagon
Correct Answer: A. dodecagon
Explanation
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
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *