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The angles of a pentagon are x°, (x + 20)°, (x + 40)°, (x + 60)° and (x + 80)°. The smallest angle of the pentagon is
(a) 75°
(b) 68°
(c) 78°
(d) 85°

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Solution

(b) 68°
Sum of all the interior angles of a polygon with n sides = $(n - 2) \times 180 °$

$∴ (5 - 2) \times 180^{o} = x + x + 20 + x + 40 + x + 60 + x + 80 \Rightarrow 540 = 5 x + 200 \Rightarrow 5 x = 340 \Rightarrow x = 68^{o}$

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