Geometry has been relegated to only 10% of the SAT but it still composes 15% to 20% of the ACT. You may need to know the sum of the interior angle measurements of regular polygons on both tests, but no formulas are provided on either. So how should you prepare for these types of questions?
The easiest way to find these sums is to memorize the following table:
Do you notice a pattern in the table? For every side that is added, another 180º is added to the sum of the interior angles!
If you are unable to memorize the sums of the interior angles in this table, there is a trick to help you calculate them for any regular polygon. First, divide the polygon into triangles with a common vertex. Then, because the interior angles of a triangle equal 180°, multiply the number of triangles within the polygon by 180°:
You may be wondering how this will help on the SAT or ACT. Once you have the sum of the interior angles of a regular polygon, you can determine the measurement of each angle. Divide the sum by the number of angles:
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