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°
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 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 sides of the polygon is 6.