If the angles are congruent and sum to 180, then each measures half of 180, or 90. By definition an angle that measures 90 is a right angle, so both are right angles.
Work Step by Step
By the definition of congruent, $m\angle ABC=m\angle XYZ$. $m\angle ABC+m\angle XYZ=180\longrightarrow$ is given $m\angle ABC+m\angle ABC=180\longrightarrow$ substitution $2m\angle ABC=180\longrightarrow$ combine like terms $m\angle ABC =90\longrightarrow$ division property of equality $m\angle XYZ=90\longrightarrow$ transitive property of equality