Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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How is the number of diagonals in a polygon calculated?

n(n+2)/2
n(n-2)/2
n(n-1)/2
n(n-3)/2

The correct answer is: n(n-3)/2

To find the number of diagonals in a polygon, one must understand the relationship between the number of sides of the polygon (denoted as $ n $) and the diagonals. The formula used to calculate the number of diagonals in any polygon is given by $ \frac{n(n-3)}{2} $. Here’s how this formula works: 1. Each vertex of a polygon can connect to $ n-1 $ other vertices, creating potential connections. Among these connections, three sides are not considered diagonals because they connect to adjacent vertices (the sides of the polygon itself). 2. Therefore, each vertex can connect to $ n-3 $ vertices to form a diagonal. 3. Since a polygon has $ n $ vertices, multiplying them yields $ n(n-3) $. However, this count includes each diagonal twice (once from each endpoint of the diagonal), so we divide the total by 2, leading us to the formula $ \frac{n(n-3)}{2} $. This understanding reveals why this particular option, which represents the formula correctly, is the right choice.