## Task 3 - 320613

Given are two angles $B A C$ and $E D F$ with measures $\alpha+\beta$ and $\alpha-\beta$ respectively (see figure).

Construct two angles with measures $\alpha$ and $\beta$ using only a compass and a straightedge.

Describe how you found the construction.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0280.jpg?height=317&width=620&top_left_y=1800&top_left_x=1158)
If one adds or subtracts the angle measures $\alpha+\beta$ and $\alpha-\beta$, one obtains $2 \alpha$ or $2 \beta$, respectively. Accordingly, by applying the angle with the measure $\alpha-\beta$ to the ray $A B^{+}$ or $A C^{+}$, one can draw angles with the measures $2 \alpha$ or $2 \beta$, respectively. These angles can be bisected to obtain angles with the measures $\alpha$ or $\beta$, respectively.