A regular polygon has angles of size 150° . How many sides does the polygon have ?
Let n be the number of sides of the polygon. The formula for the sum of the interior angles of a polygon is (n-2) x 180°. Since each angle in our polygon is 150°, the sum of all angles is n x 150°. Therefore, we have:
n x 150° = (n-2) x 180°
Multiplying out, we get:
150n = 180n - 360
Solving for n, we get:
30n = 360
n = 12
Therefore, the polygon has 12 sides.
To determine the number of sides of a regular polygon with angles of size 150°, we can use the formula:
n = 360° / angle size
where n represents the number of sides of the polygon.
Substituting the given angle size of 150° into the formula:
n = 360° / 150°
Simplifying:
n = 2.4
Since the number of sides must be a whole number, we can conclude that the polygon has 2.4 sides. However, since a polygon must have a whole number of sides, we round down to the nearest whole number.
Thus, the polygon has 2 sides.