The angles of a pentagon in degrees are y°, (y+20°), (y+40°), (y+60°) and (y+80°). The smallest angle of the pentagon is:

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The angles of a pentagon in degrees are y°, (y+20°), (y+40°), (y+60°) and (y+80°). The smallest angle of the pentagon is:

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88°

78°

68°

58°

answer is C.

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Detailed Solution

Now, let's find the sum of the interior angles in a pentagon.
Sum of interior angles = (n−2) × 180°
Here, n = 5,
⇒Sum of interior angles = (5−2) × 180° = 3 × 180°
⇒Sum of interior angles = 540°
According to conditions,
y° + (y+20°) + (y+40°) + (y+60°) + (y+80°) = 540°
⇒5y + 200° = 540°
⇒5y             = 540°− 200°
⇒y               = 340°5
⇒y               = 68°
Out of the five angles given in the pentagon, the smallest angle is y. So the smallest angle of the pentagon is going to be 68° .

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