B1. Seven equally long matches lie on the table and touch each other as shown in the figure. How many degrees is the indicated angle?

![](https://cdn.mathpix.com/cropped/2024_04_17_fae9e9df1e99e6590d6bg-2.jpg?height=271&width=285&top_left_y=1315&top_left_x=1411)
B1. 100 The outer four matches form a parallelogram. The four base angles of the two indicated isosceles triangles are therefore all equal, say $\alpha$ and equal to 180 degrees minus the desired angle. The three matches in the middle form an equilateral triangle (with angles of 60 degrees). The sum of the angles of a triangle is 180 degrees, so $(180-\alpha)+2(120-\alpha)=180$.

![](https://cdn.mathpix.com/cropped/2024_04_17_eb67361d5b5f4c2be0e0g-2.jpg?height=255&width=309&top_left_y=1029&top_left_x=1496)
We find $\alpha=80$ so that the desired angle is 100 degrees.