Question

Two circles intersect each other at c and d line ab is their common tangent to prove angle acb+angle adb=180 degree

Answer 1

Answer:

∠ADB+ ∠ACB= 180°

Step-by-step explanation:

Here given information concludes that

∠CBA= ∠CDB

∠CAB = ∠CDA

∠CDB+ ∠CDA= ∠CBA+∠CAB .......... EQUATION (1)

∠CBA+ ∠CAB+ ∠ACB= 180 °

∠CBA+ ∠CAB=180-∠ACB ...........EQUATION (2)

Equation both equations (1) & (2)

∠CDB+ ∠CDA= 180-∠ACB

Here,  

∠CDB+ ∠CDA= ∠ADB ..............EQUATION (3)

PUTTING THE VALUE IN ABOVE EQUATION

∠ADB= 180-∠ACB

∠ADB+ ∠ACB= 180°

HENCE PROVED.