Problem 4. The difference between angle $\alpha$ and its supplementary angle $\beta$ is $56^{\circ}$. Calculate the complementary angle $\gamma$ of angle $\beta$.
Solution. Let $\alpha$ and $\beta$ be consecutive angles that satisfy the condition in the problem. If we construct the difference $\alpha-\beta$ as shown in the diagram, it follows that $\beta+(\alpha-\beta)+\beta=180^{\circ}$. Therefore, $2 \beta+56^{\circ}=180^{\circ}$, and from this $\beta=(180^{\circ}-56^{\circ}): 2=62^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_06_05_d4fd26fa5c16caf575adg-3.jpg?height=226&width=474&top_left_y=543&top_left_x=1008)
Then $\gamma=90^{\circ}-62^{\circ}=28^{\circ}$.