The sum of the interior and exterior angles of a regular polygon is always 180°. So, we can set up the equation:
(7x + 44) + (x + 8) = 180
Combine like terms:
8x + 52 = 180
Subtract 52 from both sides:
8x = 128
Divide both sides by 8:
x = 16
We know that the number of sides in a regular polygon can be found using the formula:
n = 360° / interior angle
So, in this case:
n = 360° / (7x + 44)
n = 360° / (7*16 + 44)
n = 360° / (112 + 44)
n = 360° / 156
n ≈ 2.3
Since number of sides should be a positive integer, the closest positive integer to 2.3 is 2.
However, there must be a mistake on the original equation given (7x + 44)° (x+8)°, as a regular polygon can't have one degree for interior angle and other for the exterior ones.
