How many degrees does the angle $\alpha$ in the figure measure?
(a) 20
(b) 25
(c) 30
(d) 35
(e) 40

![](https://cdn.mathpix.com/cropped/2024_05_01_30c9a294a58a6e4b8190g-010.jpg?height=258&width=462&top_left_y=1664&top_left_x=1365)
The correct option is (a).

The internal angles of the given quadrilateral are $50^{\circ}, 180^{\circ}-30^{\circ}=150^{\circ}, \alpha$ and $180^{\circ}-40^{\circ}=140^{\circ}$. Since the sum of the internal angles of a quadrilateral is $360^{\circ}$, we have $50^{\circ}+150^{\circ}+\alpha+140^{\circ}=360^{\circ}$, from which $\alpha=20^{\circ}$.