1. **Find the measure of arc ZWX (mZWX).** Given: Angle near chord is 115°. Step 1: Recall the theorem that the measure of an inscribed angle is half the measure of its intercepted arc. Step 2: Use the formula: $$\text{Inscribed angle} = \frac{1}{2} \times \text{measure of intercepted arc}$$ Step 3: Let the inscribed angle be 115°, then: $$115 = \frac{1}{2} \times mZWX$$ Step 4: Multiply both sides by 2: $$2 \times 115 = \cancel{2} \times \frac{1}{2} \times mZWX$$ $$230 = mZWX$$ Step 5: The measure of arc ZWX is 230°. **Final answer:** $$mZWX = 230^\circ$$