2023
Mathematics
67ca00ce0c643c71d77dee1f
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: dodecagon
Explanation
An interior angle of a regular polygon = ((2n−4)×90)/n An exterior angle of a regular polygon = 360/n ((2n−4)×90)/n = 5 × 360/n (Given) = (2n-4) x 90 = 5 x 360 = 180n - 360 = 1800 = 180n = 1800 + 360 = 180n = 2160 = n = 2160/180 = 12 The polygon has 12 sides which is dodecagon
An interior angle of a regular polygon = ((2n−4)×90)/n An exterior angle of a regular polygon = 360/n ((2n−4)×90)/n = 5 × 360/n (Given) = (2n-4) x 90 = 5 x 360 = 180n - 360 = 1800 = 180n = 1800 + 360 = 180n = 2160 = n = 2160/180 = 12 The polygon has 12 sides which is dodecagonTHIS WEEK's
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