In figure if AD = 6 cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48°. Find ∠ABC

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

To find: ∠ABC

Explanation:

From 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 in the above equation, we get

And

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

We know that

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

Hence from equation (iii),

DE||BC……(iv)

Now taking AB as the transversal line, ∠ADE and ∠ABC form corresponding angles, and we know corresponding angles are equal, hence

∠ABC = ∠ADE

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

∠ABC = 48°

This is the required value.