Based on the given image, you have:
statement justification
PQ = OQ given
m∠1 = m∠2 given
m∠1 + m∠AXO = 180 supplementary angles
m∠2 + m∠OQB = 180 supplementary angles
m∠AXO = m∠OQB congruent angles
m∠AOX = m∠QOB congruent angles
m∠XAO + m∠AOX + m∠AXO = 180 sum of internal angles of a triangle
m∠OQB +m∠QOB + m∠QBO = 180 sum of internal angles of a triangle
m∠XAO = m∠QBO congruent angles
m∠XAO = m∠QBO is the same as ∠A = ∠B
For the steps which involve supplementary angles you consider that if m∠1 = m∠2 it is necessary that m∠AXO = m∠OQB.
For the steps which involve the sum of internal triangle, you consider if m∠AXO = m∠OQB and m∠AOX = m∠QOB it is necessary m∠XAO = m∠QBO