[Angle between two chords and two secants]

A circle is divided by points $A, B, C, D$ such that $\sim A B:-B C:-C D:-D A=2: 3: 5: 6$. Chords $A C$ and $B D$ are drawn, intersecting at point $M$.

Find the angle $A M B$.
$$
\angle A M B=\frac{1}{2}(\smile A B+\smile C D)=\frac{7}{2+3+5+6} \cdot \frac{1}{2} \cdot 360^{\circ}=78^{\circ} 45^{\prime}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_4541620ef230b5fef331g-17.jpg?height=463&width=506&top_left_y=0&top_left_x=776)

## Answer

$78^{\circ} 45^{\prime}$.