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.

1 answer

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.