Given information:

The given expression transitive property of angle congruence.

Calculation:

Calculate the transitive property of equality.

\(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\),

\(\displaystyle\angle{2}\stackrel{\sim}{=}\angle{3}\)

\(\displaystyle{m}\angle{1}={m}\angle{2}\)

\(\displaystyle{m}\angle{2}={m}\angle{3}\)

\(\displaystyle{m}\angle{1}={m}\angle{3}\)

\(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{3}\)

Therefore, the angle of congruence is \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{3}\).

The given expression transitive property of angle congruence.

Calculation:

Calculate the transitive property of equality.

\(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\),

\(\displaystyle\angle{2}\stackrel{\sim}{=}\angle{3}\)

\(\displaystyle{m}\angle{1}={m}\angle{2}\)

\(\displaystyle{m}\angle{2}={m}\angle{3}\)

\(\displaystyle{m}\angle{1}={m}\angle{3}\)

\(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{3}\)

Therefore, the angle of congruence is \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{3}\).