Q. 53.8( 5 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: 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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses