Complementary angles are two angles that add up to a right angle, or 90°.
If ∠A and ∠B are complementary, that means that m∠A + m∠B = 90°. Plugging in the given values for m∠A and m∠B, we have
(2x-29) + (x + 23) = 90
Which we can use to solve for x:
2x - 29 + x + 23 = 90
(2x + x) + (-29 + 23) = 90
3x - 6 = 90
3x = 96
x = 32
Since we already know m∠B = (x + 23)°, we can substitute x to find that m∠B = (32 + 23)° = 55°