1. **State the problem:** We are given that ray RT bisects angle \(\angle QRS\), meaning it divides \(\angle QRS\) into two equal angles. The measure of \(\angle QRS\) is 122 degrees, and the measure of \(\angle SRT\) is given by \(4x + 33\). We need to find the value of \(x\). 2. **Recall the angle bisector property:** If ray RT bisects \(\angle QRS\), then \(\angle QRT = \angle SRT\). 3. **Express the angles:** Since \(\angle QRS = 122^\circ\), and RT bisects it, each of the two smaller angles is half of 122 degrees: $$\angle QRT = \angle SRT = \frac{122}{2} = 61^\circ$$ 4. **Set up the equation:** We know \(\angle SRT = 4x + 33\), so: $$4x + 33 = 61$$ 5. **Solve for \(x\):** $$4x = 61 - 33$$ $$4x = 28$$ $$x = \frac{28}{4} = 7$$ 6. **Final answer:** \(x = 7\).