Question

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Answer 1

Look at the pair of similar triangles CDO and ABO. By AA postulate, both are smiliar. The ratio of similarity is equal on the corresponding sides.

(ratio of corresponding side lengths)

$\implies(x-2):(x-1)=(x+3):(x+5)$

(product of extremes and means)

$\implies x^{2}+3x-10=x^{2}+2x-3$

$\implies 3x-2x=-3+10$

$\implies x=7$

The value of $x$ is 7.