Angle ABC in the triangle is 69.3 degrees
How to find the angle
The angle is calculated using cosine rule
cos (Angle B) = (b² - a² - c²) / (-2 * a * c)
where
a = BC = 2
b = AC = AM + MC = 2
c = AB = √2
cos (Angle B) = (2² - 2² - (√2)²) / (-2 * 2 * √2)
cos (Angle B) = (4 - 4 - 2) / (-4√2)
cos (Angle B) = 1 / (2√2)
cos (Angle B) = √2 / 4
Angle B = arcos (√2 / 4)
Angle B = 69.3 degrees