How many diagonals does a pentagon have?

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Study for the NBCT Mathematics AYA Component 1 exam. Utilize flashcards and multiple-choice questions with detailed explanations for each question. Prepare efficiently for success in your teaching certification journey!

Multiple Choice

How many diagonals does a pentagon have?

Explanation:
Diagonals are lines that connect two non-adjacent vertices of a polygon. In any n-gon, each vertex can connect by a diagonal to n−3 other vertices (you can’t connect to itself or to its two neighbors). Counting each diagonal from both ends would double-count, so the total number of diagonals is n(n−3)/2. For a pentagon, that’s 5(5−3)/2 = 5 diagonals. You can see this by listing them: from one vertex you can connect to two non-adjacent vertices, and repeating around the shape gives five diagonals in total.

Diagonals are lines that connect two non-adjacent vertices of a polygon. In any n-gon, each vertex can connect by a diagonal to n−3 other vertices (you can’t connect to itself or to its two neighbors). Counting each diagonal from both ends would double-count, so the total number of diagonals is n(n−3)/2. For a pentagon, that’s 5(5−3)/2 = 5 diagonals. You can see this by listing them: from one vertex you can connect to two non-adjacent vertices, and repeating around the shape gives five diagonals in total.

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