Find the angle $\mathrm{AGE}$ in the regular dodecagon shown below.

Find the angle $\mathrm{AHE}$ in the regular dodecagon shown below.

Find the angle $\mathrm{AHC}$ in the regular dodecagon shown below.

In the following figure the three equispaced vertices of a regular dodecagon are connected in such a way that they create a triangle, as shown below. If each side of the triangle is $\sqrt{3}\sqrt{2+\sqrt{3}} \mathrm{cm}$, find the circumradius of the dodecagon.

In the following figure the four equispaced vertices of a regular dodecagon are connected in such a way that they create a quadrilateral, as shown below. If each side of the quadrilateral is $\sqrt{3}+1 \mathrm{cm}$, find the circumradius of the dodecagon.