Given :
▪︎Measure of ∠G = 64°
▪︎△GAM is an isosceles triangle.
We know that :
▪︎The opposite base angles of an isosceles triangle are always equal.
Let the measure of ∠A be x.
Then, the measure of ∠M will also be x.
Which means :
[tex] = \tt64 + x + x = 180[/tex]
[tex] = \tt64 + 2x = 180[/tex]
[tex] = \tt2x = 180 - 64[/tex]
[tex] =\tt 2x = 116[/tex]
[tex] =\tt x = \frac{116}{2} [/tex]
[tex] = \tt \: x = 58[/tex]
Since the sum of all these angles is equivalent to 180°[64+58+58=180], we can conclude that we have found out the correct measure of each of these angles.
▪︎Therefore :
Measure of ∠A = 58°
Measure of ∠M = 58°
