1. **State the problem:** We need to find the measure of angle $\angle CEF$ given the angles around points $C$ and $E$ with expressions involving $x$ and $y$. 2. **Identify the given angles:** - At point $C$, angles $98^\circ$ and $(x+y)^\circ$ are vertical angles, so they are equal. - At point $E$, angles $y^\circ$ and $(2x+8)^\circ$ are vertical angles, so they are equal. 3. **Write equations from vertical angles:** $$ (x+y) = 98 $$ $$ y = 2x + 8 $$ 4. **Substitute $y$ from the second equation into the first:** $$ (x + (2x + 8)) = 98 $$ $$ 3x + 8 = 98 $$ 5. **Solve for $x$:** $$ 3x = 98 - 8 $$ $$ 3x = 90 $$ $$ x = \cancel{\frac{3x}{3}}{\frac{90}{3}} = 30 $$ 6. **Find $y$ using $y = 2x + 8$:** $$ y = 2(30) + 8 = 60 + 8 = 68 $$ 7. **Find $m\angle CEF$ which is $y^\circ$:** $$ m\angle CEF = 68^\circ $$ **Final answer:** $$ m\angle CEF = 68^\circ $$