In the figure (1) given below, ∠AED = ∠ABC. Find the values of x and y.

Considering △ABC and △ADE,

∠AED = ∠ABC (Given)

∠A = ∠A (Common angles)

Hence by AA axiom △ABC ~ △ADE.

Since, triangles are similar so ratio of their corresponding sides will be equal.

$\Rightarrow \dfrac{AD}{AC} = \dfrac{DE}{BC} \\[1em] \Rightarrow \dfrac{AD}{AE + EC} = \dfrac{DE}{BC} \\[1em] \Rightarrow \dfrac{3}{4 + 2} = \dfrac{y}{10} \\[1em] \Rightarrow \dfrac{3}{6} = \dfrac{y}{10} \\[1em] \Rightarrow y = \dfrac{30}{6} \\[1em] \Rightarrow y = 5.$

Similarly,

$\Rightarrow \dfrac{AB}{AE} = \dfrac{BC}{DE} \\[1em] \Rightarrow \dfrac{AD + DB}{AE} = \dfrac{BC}{DE} \\[1em] \Rightarrow \dfrac{3 + x}{4} = \dfrac{10}{y} \\[1em] \Rightarrow \dfrac{3 + x}{4} = \dfrac{10}{5} \\[1em] \Rightarrow 3 + x = \dfrac{40}{5} \\[1em] \Rightarrow 3 + x = 8 \\[1em] \Rightarrow x = 5.$

Hence, the value of x = 5 and y = 5.