Problem 8. Given an isosceles triangle $X Y Z(X Y=Y Z)$ with the angle at the vertex equal to $96^{\circ}$. Point $O$ is located inside triangle $X Y Z$ such that $\angle O Z X=30^{\circ}$, and $\angle O X Z=18^{\circ}$. Find the measure of the angle $\angle Y O X$.
Answer: $78^{\circ}$.

Solution. Let $Y H$ be the height/median/bisector of the triangle. Let $S$ be the intersection of ray $Z O$ and segment $Y H$. Note that $X S=S Z$. For example, since in triangle $X S Z$ the median $S H$ coincides with the height.

![](https://cdn.mathpix.com/cropped/2024_05_06_5f8906e33c6403142659g-23.jpg?height=689&width=1380&top_left_y=929&top_left_x=338)

Let's calculate the angles: