ABCDE is a regular pentagon.the bisector of angle A of the pentagon meets the side CD in M.Show that angle AMC =360

We know that, the measure of each interior angle of a regular pentagon is 108 degree.

Therefore, angle BAM =1/2*108 = 54 degree

Since, the sum of the angles of a quadrulateral is 360 degree. 

Therefore, in quadrilateral ABCM, we have

angle BAM+ angle ABC+ angle BCM+ angle AMC = 360 degree

54 degree+ 108 degree+ 108 degree+ angle AMC = 360 degree

angle AMC = 90 degree


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