The total measurement of all the interior angles of a regular polygon is equal to 10 right angle. Find out which Kind of polygon it is.

# The total measurement of all the interior angles of a regular polygon is equal to 10 right angle. Find out which Kind of polygon it is.

1. A
Decagon
2. B
Hexagon
3. C
Pentagon
4. D
Heptagon

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### Solution:

Let the polygon be on the n-side. It has n interior angles
we know that the sum of all the interior angles of n sided regular polygon is (n – 2) π
So, each interior angle becomes  we know that the sum of all exterior angles is 2π which is independent of the side number of a polygon?.
It's given that the total measurement of all the interior angles of the n-sided regular polygon  is equal to 10 right angles.
10 right angle are equal to
= 5π
Now, we equate the linear function of n with 5π .
so. (n – 2) π = 5π
n – 2 = 5
n = 5 + 2
n = 7

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