In the star $A B C D E$ of the given figure, it is known that $G \widehat{B} F=20^{\circ}$ and $G \widehat{H} I=$ $130^{\circ}$. What is the value of the angle $J \widehat{E} I$ ?

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-033.jpg?height=532&width=697&top_left_y=1770&top_left_x=768)
Observe that $J \widehat{E} I=B \widehat{E} H$.

In the triangle $\triangle B E H$ we have

$$
20^{\circ}+130^{\circ}+B \widehat{E} H=180^{\circ}
$$

therefore,

$$
J \widehat{E} I=B \widehat{E} H=30^{\circ}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-110.jpg?height=409&width=552&top_left_y=612&top_left_x=1226)