Question

Help, please show how to find x, thank you

Answer 1

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?


`\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 \\\\\\ 25=4x\implies \cfrac{25}{4}=x\implies 6(1)/(4)=x`