Q] express in degrees and radians,the interior angles of a regular

a]pentagon

b]hexagon

c]octagon

d]polygon of 15 sides...

For N-sided polygon,

sum of interior angles is (2n-4)*90 degrees

also Pi radians = 180 degrees

a) pentagon (n=5)

sum of interior angles = 540 deg

since its regular pentagon, each interior angle is same = 540/5 =108 degres = 1.884 radians

b) hexagon (n=6)

sum of interior angles = 720 deg

since its regular hexagon, each interior angle is same = 720/6 =120 degres = 2.093 radians

c) octagon (n=8)

sum of interior angles = 1080 deg

since its regular hexagon, each interior angle is same = 1080/8 =135 degres = 2.355 radians

d) polygon (n=15)

sum of interior angles = 2340 deg

since its regular hexagon, each interior angle is same = 2340/15 =156 degres = 2.721 radians

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Naga Ramesh
IIT Kgp - 2005 batch

For N-sided polygon,sum of interior angles is (2n-4)*90 degreesalso Pi radians = 180 degreesa) pentagon (n=5)sum of interior angles = 540 degsince its regular pentagon, each interior angle is same = 540/5 =108 degres = 1.884 radiansb) hexagon (n=6)sum of interior angles = 720 degsince its regular hexagon, each interior angle is same = 720/6 =120 degres = 2.093 radiansc) octagon (n=8)sum of interior angles = 1080 degsince its regular hexagon, each interior angle is same = 1080/8 =135 degres = 2.355 radiansd) polygon (n=15)sum of interior angles = 2340 degsince its regular hexagon, each interior angle is same = 2340/15 =156 degres = 2.721 radians----Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best.