Loading...
GRE
GRE Quantitative Reasoning Section

Comparison of Interior Angles in Polygons

Very Hard Geometry Polygons

Consider a polygon with 7 sides (heptagon) where each interior angle is equal in measure. The formula to calculate the measure of each interior angle of a regular polygon is given by:

$$ ext{Interior Angle} =\frac{(n - 2) imes 180^ ext{o}}{n}$$

where $n$ is the number of sides. Calculate the measure of each interior angle of the heptagon and then determine the sum $S$ of the measures of its interior angles. Subsequently, if one were to construct a new polygon by increasing the number of sides to 10 (decagon) while maintaining the property of equal interior angles, what would be the relationship between the sum $S$ from the heptagon and the sum of the interior angles of the decagon, denoted as $S'$. Provide answers in relation to Quantity A and Quantity B:

Quantity A: The sum of the interior angles of the heptagon.

Quantity B: The sum of the interior angles of the decagon.

Hint

Submitted6.4K
Correct4.0K
% Correct63%