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A conjecture and the flowchart proof used to prove the conjecture are shown.
Given: AB || XC
Prove: m∠1 + m∠2 + m∠3 = 180°

Drag and drop each statement to each box to complete the proof​

A conjecture and the flowchart proof used to prove the conjecture are shownGiven AB XCProve m1 m2 m3 180Drag and drop each statement to each box to complete the class=

Respuesta :

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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