# Is the sum of the angles of any polygon 1600°? How about 900°?

Given: Sum of the angles = 1600° and 900°

Sum of the angles of n-sided polygon = (n – 2) × 180°

1600° = (n – 2) × 180° 8.89 = n – 2

n = 8.89 + 2

n = 10.89

There is no polygon which have sum of the angles as 1600°.

When sum is 900°

Sum of the angles of n-sided polygon = (n – 2) × 180°

900° = (n – 2) × 180° 5 = n – 2

n = 5 + 2

n = 7

The number of sides of polygon having sum of the angles of 900° is 7 sides.

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