Express the angular measurement of the angle of a regular decagon in degrees, grades and radians.
Munni Charlie Mody
Asked: 3 years ago2022-11-07T02:31:32+05:30
2022-11-07T02:31:32+05:30In: Class 11
Express the angular measurement of the angle of a regular decagon in degrees and radian.
Express the angular measurement of the angle of a regular decagon in degrees and radian.
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We know that the angle of an n sided regular Polygon is equal to \((\frac{2n-4}{n})\) right angles.
Let θ be the angle of a regular decagon. Then,
\(θ=(\frac{2\times10-4}{10})=\frac{8}{5}\) right angles
\(\therefore θ=(\frac{8}{5}\times90)^°=144^°\) [∴ 1 right angle = 90°]
Also, \(\thereforeθ=(\frac{8}{5}\times100)=160^g\) [∴ 1 right angle = 100g ]
And \(θ=(\frac{8}{5}\times\frac{\pi}{2})^c=(\frac{4\pi}{2})^c\)
[∴ 1 right angle = \((\frac{\pi}{2})^c\) ]