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

1 answer:

amm18123 years ago

7 0

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.

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