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=360∘⇒54∘+108∘+108∘+∠AMC=360∘⇒∠AMC=360∘−270∘⇒∠AMC=90∘.