In the diagram, $H F=H G$ and $J F G$ is a straight line segment. The value of $x$ is
(A) 45
(B) 35
(C) 55
(D) 60
(E) 40

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-068.jpg?height=375&width=471&top_left_y=837&top_left_x=1247)
Since $J F G$ is a straight line, then $\angle H F G=180^{\circ}-\angle H F J=180^{\circ}-110^{\circ}=70^{\circ}$.

Since $\triangle F G H$ is isosceles with $H F=H G$, then $\angle H G F=\angle H F G=70^{\circ}$.

Since the sum of the angles in $\triangle F G H$ is $180^{\circ}$, then $70^{\circ}+70^{\circ}+x^{\circ}=180^{\circ}$, and so $140+x=180$ or $x=40$.

ANSWER: (E)