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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.
As the pentagon is convex, a+4d<180o(2)
From (1) and (2)
216a<180o
a>36o

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