Given that the opposite sides of the inner angles a, B and C in the acute angle △ ABC are a, B and C respectively, and a & # 178; + B & # 178; = C & # 178; + AB, find the value of angle C,

Given that the opposite sides of the inner angles a, B and C in the acute angle △ ABC are a, B and C respectively, and a & # 178; + B & # 178; = C & # 178; + AB, find the value of angle C,

Because COSC = (a ^ 2 + B ^ 2-C ^ 2) / 2Ab
a^2+b^2=c^2+ab
So: A ^ 2 + B ^ 2-C ^ 2 = ab
So COSC = AB / 2Ab = 1 / 2
So angle c = 60 degrees