Step-by-step explanation:
ΔACX is an isosceles triangle, so ∠AXC = ∠XAC. We'll call the measure of this angle x°.
∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180. That means ∠BXC = 180 − x.
ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB. We'll call the measure of this angle y°.
Angles of a triangle add up to 180, so:
y + y + (180 − x) = 180
2y = x
y = x/2
∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.
x + y = 90
x + x/2 = 90
3/2 x = 90
x = 60
Therefore, ∠AXC = ∠XAC = 60°.
