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Question

Question 159
ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find AMC

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Solution

Given, a pentagon ABCDE. The line segment AM is the bisector of the A.
Now, since the measure of each interior angle of a regular pentagon is 108.
BAM=12×108=54
By the angle sum property of a quadrilateral, we have (in quadrilateral ABCM)
BAM+ABC+BCM+AMC=36054+108+108+AMC=360AMC=360270AMC=90.

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