1. **State the problem:** We need to find the measure of angle E in a pentagon with angles given as follows: $\angle A = 5x$, $\angle B = 152^\circ$, $\angle C = 3x - 10$, $\angle D = 125^\circ$, and $\angle E = 4x + 18$. 2. **Formula used:** The sum of interior angles of a pentagon is given by $$ (n-2) \times 180^\circ $$ where $n=5$. So, the sum is $$ (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ. $$ 3. **Set up the equation:** Sum of all angles equals 540 degrees: $$ 5x + 152 + (3x - 10) + 125 + (4x + 18) = 540. $$ 4. **Simplify the equation:** $$ 5x + 152 + 3x - 10 + 125 + 4x + 18 = 540 $$ $$ (5x + 3x + 4x) + (152 - 10 + 125 + 18) = 540 $$ $$ 12x + 285 = 540. $$ 5. **Solve for $x$:** $$ 12x = 540 - 285 $$ $$ 12x = 255 $$ $$ x = \frac{255}{12} = 21.25. $$ 6. **Find angle E:** $$ \angle E = 4x + 18 = 4(21.25) + 18 = 85 + 18 = 103^\circ. $$ 7. **Check options:** None of the options match 103°. Let's verify calculations carefully. Recalculate sum of constants: $$ 152 - 10 + 125 + 18 = 152 + (-10) + 125 + 18 = 152 - 10 + 125 + 18 = 285. $$ Sum of $x$ terms: $5x + 3x + 4x = 12x$. Equation: $12x + 285 = 540$ so $12x = 255$ and $x = 21.25$. Calculate angle E again: $$ 4x + 18 = 4(21.25) + 18 = 85 + 18 = 103^\circ. $$ Since 103° is not an option, check if the 111° angle inside the pentagon affects the sum. The problem states 111° is an interior angle between vertices A and F, but F is not part of the pentagon angles sum. Therefore, the 111° is not part of the pentagon's interior angles sum. Check if the problem expects angle E to be one of the options given. Since none match 103°, check if the problem expects rounding or if the question is about angle E's measure directly. Since none of the options match 103°, the closest is 126° (option c) or 135° (option d). But mathematically, angle E is 103°. **Final answer:** $\boxed{103^\circ}$ (not listed in options). Possibly a misprint or additional info needed. If forced to choose from given options, none are correct based on calculations.