To determine the number of sides of the polygon, we can use the properties of interior angles in polygons. First, we need to recall the formula for the sum of interior angles of a polygon with n sides, which is:
Sum of Interior Angles = (n – 2) × 180°
In this case, we know that four angles are each 100 degrees and the remaining angles are each 160 degrees. Let’s denote the total number of sides of the polygon as n. This means that:
Let m be the number of remaining angles:
n = 4 + m
Now, we can express the sum of all interior angles in terms of the known angles:
Sum of Interior Angles = 4 × 100° + m × 160°
Setting this equal to the formula for the sum of interior angles, we have:
4 × 100 + m × 160 = (n – 2) × 180
Substituting m = n – 4 into the equation gives:
4 × 100 + (n – 4) × 160 = (n – 2) × 180
This simplifies to:
400 + 160n – 640 = 180n – 360
Combining like terms results in:
800 = 20n
Next, we can solve for n:
n = 800 / 20 = 40
Thus, the polygon has 40 sides.