On a plane, four lines are located (see the figure). The angles between some of them are known: $\alpha=110^{\circ}, \beta=60^{\circ}, \gamma=80^{\circ}$.

Find the angles between the remaining pairs of lines.

![](https://cdn.mathpix.com/cropped/2024_05_06_d7c3832c1c4b0d15493ag-03.jpg?height=389&width=640&top_left_y=131&top_left_x=706)
Apply the theorem of the exterior angle of a triangle.

## Solution

According to the theorem of the exterior angle of a triangle, $x=\alpha-\gamma=30^{\circ}, z=\beta-x=30^{\circ}, y=\alpha-\beta=50^{\circ}$.

## Answer

$30^{\circ}, 30^{\circ}, 50^{\circ}$.