Question

How many sides does a polygon have if each of its interior angles measures

(a) 120°:
(i) 3 sides
(ii) 4 sides
(iii) 5 sides
(iv) 6 sides

Answer 1

To determine the number of sides of a polygon where each interior angle is 120°, you can use the formula for the sum of interior angles of a polygon ((n - 2) × 180° = n × interior angle). By solving for n, you find that the polygon must have 6 sides.

Step-by-step explanation:

To find out how many sides a polygon has based on the measure of its interior angles, we use the formula:

(n - 2) × 180° = n × interior angle, where n is the number of sides of the polygon.

If each interior angle measures 120°, we can set up the equation

(n - 2) × 180° = n × 120°.

Solving for n:

1. 180n - 360 = 120n
2. (180n - 120n) = 360
3. 60n = 360
4. n = 360 / 60
5. n = 6

Therefore, a polygon with interior angles of 120° must have 6 sides, making it a hexagon.