Question

In a polygon, one interior angle is 150°, and the remaining interior angles are also 150° each. How many sides does the polygon have?

A) 4
B) 5
C) 6
D) 8

Answer 1

The polygon has 3 sides.

Step-by-step explanation:

In a polygon, the sum of the interior angles can be found using the formula:

Sum of interior angles = (n - 2) * 180 degrees

Where n is the number of sides in the polygon.

Given that one interior angle is 150 degrees and the remaining interior angles are also 150 degrees each, we can set up the following equation:

150 + (n - 1) * 150 = (n - 2) * 180

Simplifying this equation, we get:

150n = 360

Dividing both sides by 150, we find:

n = 2.4

Since the number of sides must be a whole number, it means that the polygon has 3 sides.

Answer 2

The polygon with each interior angle of 150° has 12 sides and is called a dodecagon. This was calculated using the sum of interior angles formula (n-2)x180°, where 'n' represents the number of sides.

Step-by-step explanation:

To determine the number of sides in a polygon where each interior angle is 150°, we can use the formula for the sum of interior angles of a polygon, which is (n-2)×180°, where ‘n’ is the number of sides. So, we set up the equation:

(n-2)×180 = n×150.

Expanding and solving for ‘n’ gives us:

180n - 360 = 150n,

which simplifies to:

30n = 360,

and further to:

n = 12.

Therefore, the polygon must have 12 sides, which means it is a dodecagon.