A closed polygon has six sides and one of its angles is 30 deg greater than each of the other five e...........

Quantitative Aptitude (CDS) Coordinate Geometry

A closed polygon has six sides and one of its angles is 30° greater than each of the other five equal angles. What is the value of one of the equal angles?

55°

115°

150°

175°

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Explanation:

For finding the sum of the interior angles of a polygon is the same, whether the polygon is regular or irregular.
So, we would use the formula (n — 2) x 180°.
Where n is the number of sides in the polygon.
Let one angle of the polygon be x and other 5 equal angles be y.
According to the question,
x = y + 30…….(i)
(n - 2)×1800 = x + 5y……(ii)
From (i) and (ii), we get
(n - 2)×1800 = y + 30 + 5y
=>(6 - 2) ×1800 = 30 + 6y
=>4×1800 = 30 + 6y
=>6y = 690
=>y = 690 / 6=115^o
Hence value of equal angles be 115^o