Answer

Given: ∠A = ∠CED

To prove: Δ CAB ∼ Δ CED

To find: The value of x.

Theorem Used:

If two triangles are similar, then the ratio of their corresponding sides are equal.

Explanation:

We have, ∠A = ∠CED

In ΔCAB and ΔCED

∠C = ∠C (Common)

∠A = ∠CED(Given)

Then, ΔCAB ~ ΔCED(By AA similarity)

As corresponding parts of similar triangle are proportional.

So,

Substituting the given values, we get,

⇒ 15x = 90

⇒ x = 90/15

⇒ x = 6 cm

OR

We have, DE||BC, AB = 6cm and AE = 1/4 AC

In ΔADE and ΔABC

∠A = ∠A (Common)

∠ADE = ∠ABC (Corresponding angles)

Then, ΔADE ~ ΔABC (By AA similarity)

So, (Corresponding parts of similar triangle area proportion)

Or (AE = 1/4 AC Given)

Or,

Or, AD = 6/4

Or, AD = 1.5cm