## Task 1 - 080811

The figure shows a five-pointed star, where the points $A, B, C, D, E$ are the vertices of a regular pentagon.

Determine the size of the angle $\angle A C E$!

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0621.jpg?height=354&width=352&top_left_y=448&top_left_x=1366)
Let $M$ be the circumcenter of the pentagon $ABCDE$. The angle $\angle ACE$ is an inscribed angle to the central angle $\angle AME$ and is therefore half the size of this angle.

Since the pentagon is regular, this central angle is $72^{\circ}$. Thus, the angle $\angle ACE$ has a size of $36^{\circ}$.