Is -6.743743… a rational or irrational number? Your

Rational because .743 repeats

Rational because the 6 is negative

Irrational because the number never ends

Irrational because the 6 is negative

It's rational because it contains a repeating digit pattern, 743 (first option).

In particular, if

x = -6.743743…,

then

1000x = -6,743.743743… .

Subtracting, we can eliminate the trailing end and solve for x exactly:

1000x - x = -6,743.743743… - (-6.743743…)

999x = -6,737

x = -6,737/999

1. Definition of Supplementary Angles; 2. Transitive Property

Step-by-step explanation:

Statement Justification:

line AB ∥ line EF  ⇒ (Given)

m∠KLF = 116°       ⇒ (Given)

m∠KLF+ m∠BKL = 180° ⇒ 1. (Definition of Supplementary Angles)

Definition of Supplementary angles is:

"If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees."

m∠BKL + m∠AKL = 180°  ⇒ (Linear Pair Postulate)

m∠KLF + m∠BKL = m∠BKL + m∠AKL ⇒ 2. (Transitive Property)

the transitive property states that:

"If a = b and b = c, then a = c. In other words, if a is related to b by some property, and b is related to c by the same property, then a is related to c by that property."

m∠KLF = m∠AKL   ⇒ (Subtraction Property)

m∠AKL = m∠KLF   ⇒ (Symmetric Property)

m∠AKL = 116°         ⇒ (Substitution Property)

Hence the Final Answer is:

1. Definition of Supplementary Angles; 2. Transitive Property