Answer :

**Given:** AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48°, in ΔABC in the above figure

**To find: **The value of ∠ABC.

**Explanation:**

From the given figure, we see that line DE divides the two sides of the triangle.

Now we will find the ratio of the sides, i.e., we will find

Now substituting the given values to get,

And

From equation (i) and (ii), we get

We know that

If a line divides two sides of a triangle in the same ratio then the line is parallel to the third side.

Hence from equation (iii),

DE||BC……(iv)

As AB is a transversal line so, ∠ADE and ∠ABC form corresponding angles, and we know corresponding angles are equal, hence

∠ABC = ∠ADE

Now given ∠ADE = 48°, substituting this in the above equation, we get

∠ABC = 48°

This is the required value.

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