1. **State the problem:** We have an isosceles trapezoid EFGH with $m\angle F = c + 49^\circ$ and an adjacent angle measuring $133^\circ$. We need to find the value of $c$. 2. **Recall properties of isosceles trapezoids:** In an isosceles trapezoid, the base angles are congruent, and consecutive angles between the bases are supplementary (sum to $180^\circ$). 3. **Set up the equation:** Since $\angle F$ and the adjacent angle $133^\circ$ are consecutive angles between the bases, they must satisfy: $$ (c + 49) + 133 = 180 $$ 4. **Solve for $c$:** $$ c + 49 + 133 = 180 $$ $$ c + 182 = 180 $$ $$ c = 180 - 182 $$ $$ c = -2 $$ 5. **Check the result:** A negative angle value for $c$ is not possible in this context, so re-examine the problem. Since the trapezoid is isosceles, the angles at the same base are equal. Given $m\angle F = c + 49^\circ$ and the other base angle is $133^\circ$, these should be equal: $$ c + 49 = 133 $$ 6. **Solve for $c$ again:** $$ c = 133 - 49 $$ $$ c = 84 $$ **Final answer:** $$ \boxed{84^\circ} $$