## Task 3 - 060623

Given is an angle with the degree measure $\alpha=36^{\circ}$ (see figure).

Construct, using only a compass and straightedge, an angle whose degree measure is $99^{\circ}$!

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0175.jpg?height=160&width=240&top_left_y=1762&top_left_x=1522)
The required angle can be constructed as the sum of a right angle and an angle of $9^{\circ}$.

The right angle is constructed in the usual way. Then, the given angle is bisected, and one of the two resulting angles (degree measure $\frac{\alpha}{2}=18^{\circ}$) is bisected again. This results in an angle of degree measure $\frac{\alpha}{4}=9^{\circ}$.

The right angle and the $9^{\circ}$ angle are added together in the manner specified in the textbook for grade 5, and the required angle of $99^{\circ}$ is obtained.