2. What is the degree measure of angle $\angle A$, if its bisector forms an angle with one of its sides that is three times smaller than the angle adjacent to $\angle A$?
Answer: $72^{\circ}$.

Solution. Let $x$ be the degree measure of the angle formed by the angle bisector of $\angle A$ with one of its sides. Then the degree measure of the angle $\angle A$ is $2 x$, and the degree measure of the adjacent angle is $3 x$. Therefore, $2 x+3 x=180$, from which $x=36$ and $\angle A=72^{\circ}$.