four interior angles of an irregular polygon are each 155 degrees, while the rest are each 160 degrees, find the number of sides of the polygon.
Let's use the formula for the sum of interior angles of a polygon:
Sum of interior angles = (n-2)*180
where n is the number of sides of the polygon.
We know that four interior angles are each 155 degrees, so the sum of those angles would be 4*155 = 620 degrees.
The rest of the interior angles are each 160 degrees, so we can represent the sum of those angles as (n-4)*160.
Putting it all together, we can set up the equation:
620 + (n-4)*160 = (n-2)*180
Simplifying:
620 + 160n - 640 = 180n - 360
Solving for n:
180n - 160n = 620 + 640 - 360
20n = 900
n = 45
Therefore, the polygon has 45 sides.