Problem 7.4. The figure shows 5 lines intersecting at one point. One of the resulting angles is $34^{\circ}$. How many degrees is the sum of the four angles shaded in gray?

![](https://cdn.mathpix.com/cropped/2024_05_06_4d36ea080cd7b65cb574g-4.jpg?height=504&width=515&top_left_y=91&top_left_x=469)
Answer: $146^{\circ}$.

Solution. Replace the two "upper" gray angles with their equal vertical angles, as shown in the picture:

![](https://cdn.mathpix.com/cropped/2024_05_06_4d36ea080cd7b65cb574g-4.jpg?height=513&width=519&top_left_y=811&top_left_x=465)

Now it is clear that the gray angles, together with the $34^{\circ}$ angle, sum up to $180^{\circ}$. Therefore, the sum of the gray angles is $146^{\circ}$.