Curved Surface Area & Total Surface Area of a Pyramid
The measures ...
Question
The measures of the angles of a convex pentagon are in arithmetic series. The smallest angle of the pentagon:
A
must be >36∘
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B
cannot be <36∘
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C
must be =36∘
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D
may be of any measure
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Solution
The correct option is C must be =36∘ Let the angles of a pentagon =a,a+d,a+2d,a+3d,a+4d, which are in A.P. Sum of the angles of a pentagon =540 ⇒5a+10d=540o ⇒a+2d=108o−−−−−−−−−−−−−−−(1) Let the largest angle be a+4d.