Q. 54.3( 11 Votes )

In figure if AD =

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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