Aconjecture and the flowchart proof used to prove the conjecture are shown. given: ab¯¯¯¯¯∥xc−→− prove: m∠1+m∠2+m∠3=180° a triangle with vertices labeled as a b and c. the interior angle c a b is labeled as 2, angle a c b is labeled as 1, and angle c b a is labeled as 3. line x passes through upper vertex c and forms three angles. the interior angles are labeled as angle 4 and angle 5. drag and drop a statement to each box to complete the proof.

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.

answer: a

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x