I found this problem on facebook. I have tried for hours to solve the problem but could not solve it. My approach is finding the first equation $x+y=30$. But can not find second equation. I am new here. Please help me.
2026-04-01 21:51:50.1775080310
What are the unknown angles?
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Apply the sine rule to the three triangles making up the large one to establish
$$\frac{\sin 2x}{\sin 30^\circ}\cdot \frac{\sin x}{\sin(30^\circ-x)}\cdot \frac{\sin(90^\circ-2x)}{\sin30^\circ}=1 $$
which has the solution $x= 12^\circ$, and in turn $y=18^\circ$.