Notice that ∠SQR is an exterior angle to △ QRT, so you can apply the Exterior Angle Theorem.
Statements
Reasons
RQ bisects ∠SRT
Given
∠SRQ ≅ ∠QRT
Definition of angle bisector
m∠SRQ = m∠QRT
Definition of congruent angles
∠SQR is exterior to △ QRT
From the diagram
m∠SQR > m∠QRT
Exterior Angle Theorem
m∠SQR > m∠SRQ
Substitution
Since RQ bisects ∠SRT we have that ∠SRQ ≅ ∠QRT, which means that m ∠SRQ = m ∠QRT.
Next, we notice that ∠SQR is an exterior angle to △ QRT.
Therefore, by applying the Exterior Angle Theorem, we have that m ∠SQR > m ∠QRT but, since m ∠SRQ = m ∠QRT, we obtain that m ∠SQR > m ∠SRQ.
Two-Column Proof
In the following table we summarize the proof we did before.
