Question

In figure if AD= 6cm, DB=9cm, AE = 8cm and EC = 12cm and ADE = 480

. Find ABC

Answer 1

Answer:

∠ ABC = 48°

Step-by-step explanation:

All we have to do is to prove that two triangles: ABC and ADE are similar.

We will use the proportion:

AD : AB = AE : AC

6 : ( 6 + 9 ) = 8 : ( 8 + 12 )

6 : 15 = 8 : 20,  or 120 = 120, when we cross multiply.

Therefore ΔABC is similar to ΔADE.

Also ∠ABC= ∠ADE=48°.

Answer 2

Thank you for asking this question. Here is your answer:

AD/DB = 6/9 = 2/3

AE/EC = 8/12 = 2/3

AD/DB = AE/EC

Now we will use the Proportionality Theorem

AD/DB = AE/EC

=> DE // BC

∠ADE = ∠ABC = 48° [ as DE//BC and DB is the traversal, so the angles will be equal as they are corresponding angles.

If there is any confusion please leave a comment below.