Answer :

The figure is attached below:


I have circumscribed the regular Pentagon with a circle. Since, the 360° of the circle is divided equally by the pentagon to five parts.


COD =


Using the properties of circle,


CAD = 1/2 COD


CAD = 1/2 720


CAD = 360


Now, in ∆ACD.


36° + ACD + ADC = 180°


Since, ∆ACD is an isosceles ∆,


36° + 2×ACD = 180°


ACD = 72°


Now, in ∆AMC.


MAC = 1/2 CAD = 18°


Now,


MAC + AMC + ACM = 180°


18° + AMC + 72° = 180°


AMC = 90°


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