To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, a
diagram showing the lines and their common transversal is attached.
The completed two column proof is presented as follows;
Statement
Reason
1. ∠1 and ∠2 are supplementary angles
1. Given
2. m∠1 + m∠2 = 180°
2. <u>Definition of supplementary ∠s</u>
3. ∠1 and ∠3 are supplementary angles
3. Exterior sides in opposite rays
4. <u>m∠1 + m∠3 = 180° </u>
4. <u>Definition of supplementary ∠s</u>
5. m∠1 + m∠2 = m∠1 + m∠3
5. <u>Transitive property of equality</u>
6. <u>m∠2 = m∠3 </u>
6. <u>Subtraction property of equality</u>
7. l ║ m
7. <u>Converse of alternate interior </u>
<u>angles postulate</u>
Reasons:
- Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°
- Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)
- Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles
- Reason for statement 5: Transitive property of equality describes the property that if a number <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.
- Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality
- Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.
Learn more here:
brainly.com/question/25178453
Answer:
Step-by-step explanation:
Total amount of money to be shared among Neymar, Rohit Sharma and Nadal is $250
Neymar gets two parts. This means that Neymar gets 1/2 × total amount of money.
Neymar gets 1/2 × 250 = 125
The percentage will be amount that Neymar gets divided by the total amount and multiplied by 100. It becomes
125/250 × 100 = 50%
Rohit gets three parts. This means that Rohit gets 1/3 × total amount of money.
Rohit gets 1/3 × 250 = 83.33
The percentage will be amount that Rohit gets divided by the total amount and multiplied by 100. It becomes
83.33/250 × 100 = 33.33%
Nadal gets five parts. This means that Nadal gets 1/5 × total amount of money.
Nadal gets 1/5 × 250 = 50
The percentage will be amount that Nadal gets divided by the total amount and multiplied by 100. It becomes
50/250 × 100 = 20%
Answer:
(-7)
Step-by-step explanation:
just plug in the number in the x place to solve
Answer:
x
=
37
/8
Step-by-step explanation:
Answer:
Last one
Step-by-step explanation: