Find the Number of Sides of the Polygon.


Question: Four angles of a polygon are 100° each. The remaining angles are 160° each. Find the number of sides of the polygon.

For any polygon with sides 'n', the number of interior angles will also be 'n'.

Answer: The number of sides of a polygon which has four angles of 100° measure and the rest of the angles of 160° measure is 6.

For any polygon with a number of interior angles or number of sides 'n', the sum total of all the interior angles is given as:

(n - 2) × 180°

Explanation:

Let the number of sides of the polygon be 'n'

So the number of interior angles will also be 'n'.

Now, out of 'n' interior angles, the value of 4 angles is 100°, then the number of angles with the value 160° be (n - 4).

Now since we know the total sum of all the interior angle of a polygon, let us use it to form an equation as:

4 × 100° + (n - 4) × 160° = (n - 2) × 180°

or, 400 + 160n - 640 = 180n - 360

or, 160n - 240 = 180n - 360

or, 180n -  160n = 360 - 240

or, 20n = 120

or, n = 120/20

or, n = 6

Therefore, the number of nides in the polygon is 6.