Minimum Number of Sides of a Polygon
What is the minimum number of sides a polygon can have if all its interior angles are either 167 or 168 degrees only?
Let m and k be the number of angles with values 168 & 167 respectively.
sum of the interior angles will be
168m + 167k
Counting this in a different way:
But the polygon has (m + k) sides.
So this sum of the interior angles
(n – 2) x 180
Where n = number of sides of a polygon.
In our case,
n = m + k
So, we have to solve (or find the positive integer solutions to the equation):
168m + 167k = (m + k – 2) x 180
Which is obtained by combining the two previous facts.
And among the possible integer solutions choose the one with the “smallest m + k” as the answer.
The rest of the solution is shown in the picture: