If the bisectors of two adjacent angles are perpendicular, the adjacent angles are the angles:

The sides of a quadrilateral $\mathrm{ABCD}$ are tangents to a circle at $\mathrm{L}, \mathrm{M}, \mathrm{N}$ and $\mathrm{P}$, then which of the following option is correct?

If three angles of a quadrilateral are in the ratio $3:2:1$ and the fourth angle is equal to the sum of these three, then find the value of the smallest angle.

In a cyclic quadrilateral $\mathrm{ABCD}$, $\angle \mathrm{A}=4\mathrm{x}°$, $\angle \mathrm{B}=7\mathrm{x}°,$ $\angle \mathrm{C}=5\mathrm{y}°,$ and $\angle \mathrm{D}=\mathrm{y}°$. Find the ratio $\mathrm{y}:\mathrm{x}$.