Question

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

Answer 1

Given : In ∆ABC,

AD = 6 cm , DB = 9 cm,

AE = 8 cm , EC = 12 cm

and <ADB = 48°

Now ,

AD/DB = 6/9 = 2/3 ---( 1 )

AE/EC = 8/12 = 2/3 ---( 2 )

From ( 1 ) & ( 2 ) ,

AD/DB = AE/EC

Therefore ,

DE // BC

[ By ,converse of Thales theorem ]

<ABC = <ADB = 48°

[ Corresponding angles ]