Calculate the number of sides of a regular polygon whose interior angles are each 156 degrees.
to go all the way around clockwise (360 degrees) you must turn right n times through an angle of (180 - 156)
so
n (180 - 156) = 360
n = 360/24 = 15 sides
To calculate the number of sides of a regular polygon, we can use the formula:
Number of sides = 360 degrees divided by the measure of each interior angle.
In this case, the measure of each interior angle is given as 156 degrees. So, we can substitute this value into the formula:
Number of sides = 360 degrees / 156 degrees.
Now, we can simplify this expression:
Number of sides = 2.3077.
Since a polygon cannot have a fractional number of sides, we need to round the answer to the nearest whole number. In this case, rounding 2.3077 to the nearest whole number is 2.
Therefore, the number of sides of a regular polygon with interior angles measuring 156 degrees is 2.