College Math Placement Practice Test

How many sides does a polygon have if its interior angle measures are all equal to 120 degrees?

1. 5

2. 6

3. 7

4. 8

The correct answer is: 6

To determine how many sides a polygon has when all its interior angles measure 120 degrees, we can use the formula for the interior angle of a regular polygon, which is given by: \[ \text{Interior angle} = \frac{(n-2) \times 180}{n} \] where \( n \) is the number of sides of the polygon. We want to find \( n \) such that the interior angle equals 120 degrees. Setting the equation up, we have: \[ 120 = \frac{(n-2) \times 180}{n} \] To eliminate the fraction, we can multiply both sides by \( n \): \[ 120n = (n-2) \times 180 \] Expanding the right side gives: \[ 120n = 180n - 360 \] Next, we can move terms involving \( n \) to one side of the equation: \[ 120n - 180n = -360 \] \[ -60n = -360 \] Dividing both sides by -60 gives: \[ n = \frac{360}{60} = 6 \] This shows that a