Question

A conjecture and the flowchart proof used to prove the conjecture are shown.

Answer 1

Answer:

∠1 + ∠2 + ∠3 = 180°

Step-by-step explanation:

Given :  AB II XC

To Show : ∠1 + ∠2 + ∠3 = 180°

Proof: Here, given that AB is parallel to the line XC

⇒  ∠4  =  ∠2  (Pair of Alternate angles as AB II XC)  .........  (1)

and ∠5  =  ∠3 (Pair of Alternate angles as AB II XC) ...........  (2)

Now, ∠1 + ∠4 + ∠5  = 180° ( Straight Angle)

But, from above (1) and (2)

∠1 + ∠2 + ∠3   =   180°  ( as ∠4  =  ∠2,  ∠5  =  ∠3)

Hence, ∠1 + ∠2 + ∠3   =   180°

Hence Proved.