posted by Anonymous .
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?
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.