Suppose AXB and BXC are complementary and congruent. What are their measures?

If two angles are complementary, it means that they add up to 90 degrees.

It two angles are congruent, it means that they have the same angle measure.

Let the angle measure of AXB = x

and the angle measure of BXC = y

Because the two angles are complementary i. e. they add to 90:

x + y = 90

Because the two angles are congruent i. e. they equal each other:

x = y

Plug x = y back into the first equation.

x + x = 90

x = 45

y = 45

Angles AXB and BXC are both 45 degrees.