Q. 54.3( 11 Votes )
In figure if AD =
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.
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,
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),
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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