1. **State the problem:** We need to find the value of $x$ given the angles around point $F$ where lines intersect. 2. **Analyze the figure and given information:** - Angle between line $AF$ and line $BF$ is $37^\circ$. - Angle between line $DF$ and line $CF$ is $(2x + 3)^\circ$. - There is a right angle ($90^\circ$) between line $EF$ and line $AF$. 3. **Use the fact that angles around a point sum to $360^\circ$:** The four angles around point $F$ are: - $37^\circ$ - $90^\circ$ - $(2x + 3)^\circ$ - The remaining angle, which we can call $\theta$. 4. **Identify the remaining angle $\theta$:** Since $EF$ is horizontal and $AF$ is vertical, and $BF$ and $DF$ are diagonal lines crossing at $F$, the angles $37^\circ$ and $(2x + 3)^\circ$ are opposite angles formed by the intersecting diagonal lines $BD$ and $AC$. 5. **Use vertical angles property:** Vertical angles are equal, so: $$37 = 2x + 3$$ 6. **Solve for $x$:** $$37 = 2x + 3$$ $$37 - 3 = 2x$$ $$34 = 2x$$ $$x = \frac{34}{2}$$ $$x = 17$$ 7. **Final answer:** $$\boxed{17}$$