Question

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

Answer 1

Answer:

Given: A triangle ABC in which ∠ CAB=∠2, ∠AC B=∠1,∠C BA=∠3. Also line X passes through vertex C forming three interior angles ∠1,∠4,∠5 such that AB║X C.

To prove:m∠1+m∠2+m∠3=180°

Proof: In Δ ABC,AB║X C

 ∠2=∠5 [∠2 and ∠5 are alternate angles, AB║X C, and AC is a Transversal ] ..............(1)

∠3=∠4 [∠3 and ∠4 are alternate angles ,AB║X C, and BC is a Transversal ]......................(2)

∠1,∠4 and∠5 lie on line XC.

∠1+∠4 +∠5=180°[ Linear pair axiom]

∠1+∠2+∠3=180° [ Using 2 and 3]

Hence proved.