notice the tickmark on the angles, those angles are equal to each other.
now, notice the angle at the very top, the large triangle is really sharing it with smaller-inscribed triangle, and therefore is equal on both triangles.
therefore, the larger triangle, is similar with smaller-inscribed triangle by AA.
what the dickens does that mean?
[tex]\bf \cfrac{large}{small}\qquad \cfrac{4+5}{4}=\cfrac{5+x}{5}\implies \cfrac{9}{4}=\cfrac{5+x}{5}\implies 45=20+4x
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25=4x\implies \cfrac{25}{4}=x\implies 6\frac{1}{4}=x[/tex]
