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.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5