Quantitative Literacy Practice Exam 2026 – Comprehensive Preparation Guide

To determine the number of sides in a regular polygon given the measure of an interior angle, we can use the formula for the measure of an interior angle:

\[

\text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n}

\]

where \( n \) is the number of sides in the polygon.

In this case, the interior angle is 150°. Setting up the equation:

\[

150^\circ = \frac{(n-2) \times 180^\circ}{n}

\]

To eliminate the fraction, we can multiply both sides by \( n \):

\[

150n = (n-2) \times 180

\]

Expanding the right side gives:

\[

150n = 180n - 360

\]

Now, we can rearrange the equation to isolate \( n \):

\[

360 = 180n - 150n

\]

This simplifies to:

\[

360 = 30n

\]

Dividing both sides by 30 yields:

\[

n = 12

\]

Thus, the polygon has 12 sides. A regular polygon with an interior angle of 150° will have