What is the sum of the interior angles of a quadrilateral?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

What is the sum of the interior angles of a quadrilateral?

Explanation:
Think of how many triangles fit inside a polygon. You can divide any n-sided polygon into (n−2) triangles, and each triangle has interior angles that sum to 180 degrees. So the total sum of interior angles is (n−2)×180 degrees. For a quadrilateral, n is 4, so the sum is (4−2)×180 = 360 degrees. A quick way to see it is to draw a diagonal to split the quadrilateral into two triangles; each triangle contributes 180 degrees, giving 360 degrees in total. The other numbers correspond to shapes with different numbers of sides.

Think of how many triangles fit inside a polygon. You can divide any n-sided polygon into (n−2) triangles, and each triangle has interior angles that sum to 180 degrees. So the total sum of interior angles is (n−2)×180 degrees. For a quadrilateral, n is 4, so the sum is (4−2)×180 = 360 degrees. A quick way to see it is to draw a diagonal to split the quadrilateral into two triangles; each triangle contributes 180 degrees, giving 360 degrees in total. The other numbers correspond to shapes with different numbers of sides.

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