1. **State the problem:** We are given a circle with points W, V, and X on the circumference. The arc WX measures $17x - 10$ degrees, and the inscribed angle at V intercepting arc WX measures $8x$ degrees. We need to find the measure of arc WX, denoted as $mWX$. 2. **Recall the inscribed angle theorem:** The measure of an inscribed angle is half the measure of its intercepted arc. Mathematically, if an inscribed angle measures $\theta$, and it intercepts an arc measuring $m$, then: $$\theta = \frac{m}{2}$$ 3. **Apply the formula:** Here, the inscribed angle at V is $8x$ and the intercepted arc WX is $17x - 10$. So: $$8x = \frac{17x - 10}{2}$$ 4. **Solve for $x$:** Multiply both sides by 2 to eliminate the denominator: $$2 \times 8x = 17x - 10$$ $$16x = 17x - 10$$ Subtract $17x$ from both sides: $$16x - 17x = -10$$ $$\cancel{16x} - \cancel{17x} = -10$$ $$-x = -10$$ Multiply both sides by $-1$: $$x = 10$$ 5. **Find $mWX$:** Substitute $x=10$ into $17x - 10$: $$mWX = 17(10) - 10 = 170 - 10 = 160$$ **Final answer:** $$mWX = 160^{\circ}$$