throwback Maths 13

Solution

Fromt solution diagram, we can see that the right angle in the square is composed of two angles, $\frac{360}{7}$ and $90-\frac{360}{7}$. It follows that

$$\theta = 180^\circ - \left(90 - \frac{360}{7}\right) = 90 + \frac{360}{7} = 141\frac{3}{7}$$