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