Calculation:

By SSS Congruence Theorem, prove that \(\displaystyle\triangle{Q}{S}{V}\stackrel{\sim}{=}\triangle{Q}{T}{V}\).

Then, state that \(\displaystyle\angle{Q}{S}{V}\stackrel{\sim}{=}\angle{Q}{T}{V}\).

Use the Vertical Angles Theorem, \(\displaystyle\angle{Q}{S}{V}\stackrel{\sim}{=}\angle{1},\ {\quad\text{and}\quad}\ \angle{Q}{T}{V}\stackrel{\sim}{=}\angle{2}\).

Therefore, by the Transitive Property of Congruence to prove that \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\).

By SSS Congruence Theorem, prove that \(\displaystyle\triangle{Q}{S}{V}\stackrel{\sim}{=}\triangle{Q}{T}{V}\).

Then, state that \(\displaystyle\angle{Q}{S}{V}\stackrel{\sim}{=}\angle{Q}{T}{V}\).

Use the Vertical Angles Theorem, \(\displaystyle\angle{Q}{S}{V}\stackrel{\sim}{=}\angle{1},\ {\quad\text{and}\quad}\ \angle{Q}{T}{V}\stackrel{\sim}{=}\angle{2}\).

Therefore, by the Transitive Property of Congruence to prove that \(\displaystyle\angle{1}\stackrel{\sim}{=}\angle{2}\).