## Task 1 - 070621

The lines $g_{1}, g_{2}, g_{3}$ and $g_{4}$ intersect each other in the manner shown in the figure. Of the magnitudes $\alpha, \beta, \gamma$ and $\delta$ of the angles thus formed, $\alpha=50^{\circ}, \beta=130^{\circ}$ and $\gamma=70^{\circ}$.

Determine $\delta$!

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0178.jpg?height=357&width=511&top_left_y=375&top_left_x=1229)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0178.jpg?height=322&width=505&top_left_y=770&top_left_x=273)
It is given with the designations in the figure $\alpha=\alpha^{\prime}$ as a pair of vertical angles

$\beta+\beta^{\prime}=180^{\circ}$ as a pair of supplementary angles, thus $\beta^{\prime}=180^{\circ}-\beta=50^{\circ}$, so $\beta^{\prime}=\alpha$. From this it follows that $g_{1} \| g_{2}$.

Furthermore: $\gamma=\gamma^{\prime}$ as a pair of corresponding angles of intersected parallels and $\gamma^{\prime}+\delta=180^{\circ}$ as supplementary angles.

Thus, $\delta=180^{\circ}-\gamma^{\prime}=110^{\circ}$.