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Geometry

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I don't undestand this question in my geometry textbook. Could nayone explain it to me?
Can you fit all of the interior angles of a quadrilateral around a point without overlap? What about the interior angles of a pentagon?

  • Geometry - ,

    The interior angles of a quadrilateral total to 180(4-2) = 360 degrees.

    So, yes, they will exactly fit around a point.

    However, for a pentagon, the angles total to 180(5-2) = 540 degrees, so there's no way you can draw all five angles around a point. There are only 360 degrees in a complete circle.

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