Question

In the
given figure angle ECD = angle EDC then prove that angle ECA= angle EDB
​

Answer 1

Answer:

ACD = CDB = 180°

Break it down to...

ECA+ECD = EDC+EDB = 180°

Given ECD = EDC

So substracting it from above, ECA = EDB

Answer 2

Answer:

AB is straight line

angle ECD+angleECA=180 degree equation 1 (linear pair angles)

Again angle ECD+EDB=180 degree equation 2( linear pair angle)

From equation one and two

angle ECD+ angle ECA= angle EDC+ angle EDB

angle ECD+ angle ECA= angle ECD+ angle EDB

angle ECA=angleEDB PROVED