Question

mathematical proofs: tutorial
statements\treasons
$\angle axb \cong \angle cxb$\tgiven
$m\angle axb = m\angle cxb$\tdefinition of congruence
$\angle axb$ and $\angle axy$ form a linear pair.
$\angle cxb$ and $\angle cxy$ form a linear pair.\tdefinition of linear pair
$\angle axb$ is supplementary to $\angle axy$.
$\angle cxb$ is supplementary to $\angle cxy$.\t?
$m\angle axb + m\angle axy = 180^\circ$
$m\angle cxb + m\angle cxy = 180^\circ$\tdefinition of supplementary
$m\angle cxb + m\angle axy = 180^\circ$
$m\angle cxb + m\angle cxy = 180^\circ$\tsubstitution
$\angle cxb$ is supplementary to $\angle axy$.
$\angle cxb$ is supplementary to $\angle cxy$.\tdefinition of supplementary
$\angle axy \cong \angle cxy$\tcongruent supplements theorem

Explanation:

Step1: Identify the logical link

We know linear pairs are supplementary.

Step2: State the theorem/reason

Linear pair postulate: If two angles form a linear pair, then they are supplementary.

Answer:

linear pair postulate