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(b) Can it be an interior angle of a regular polygon? Why?

5. (b) Can it be an interior angle of a regular polygon? Why?

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 The measure of an interior angle is 22°

Regular polygon has all interior angles equal.

Let number of sides and number of interior angles be n.

Sum of interior angles of a polygon = \left ( n-2 \right )\ast 180\degree

Sum of interior angles of a polygon =  \left ( n-2 \right )\ast 180\degree=\left ( n \right )\ast 22\degree

                                                            \left ( n \right )\ast 180\degree-\left ( 2 \right )\ast 180\degree=\left ( n \right )\ast 22\degree

                                                             \left ( n \right )\ast 180\degree-\left ( n \right )\ast 22\degree= 360\degree

                                                                                 \left ( n \right )\ast 158\degree= 360\degree

                                                                                                n = 2.28

Number of sides of a polygon should be integer but since it is not a integer .So, it cannot be an regular polygon with interior angle as 22\degree

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