Final answer:
The angle of 110° cannot be the interior angle of a regular polygon with an integer number of sides. By using the formula for interior angles of regular polygons and rearranging it to solve for the number of sides, it results in a non-integer value, hence not representing a possible regular polygon.
Step-by-step explanation:
The question is concerning whether a given angle of 110° is an interior angle of a regular polygon, and if so, how many sides the polygon has. To determine this, we can use the formula for the interior angles of a regular polygon, which is ((n-2) × 180) / n where n is the number of sides. By rearranging this formula to solve for n, we can find the number of sides the regular polygon would have if one of its interior angles is 110°.
Let's apply this calculation:
− ((n-2) × 180) / n = 110°
180n - 360 = 110n
180n - 110n = 360
70n = 360
n = 360 / 70
n = 5.14
Since the number of sides n must be a whole number, and 5.14 is not a whole number, the angle of 110° cannot be the interior angle of a regular polygon with integer sides. Therefore, option (a) 'Not an interior angle, not enough information to determine the sides' is the correct choice.