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Distribute 1/2 to <span>(n – 4):
</span>
<span>
Subtract (2n + 3):
</span>
<span>
Your equation should now look like this:
</span>
<span>
Combine like terms on both sides:
</span>
<span>
Subtract 1/2n from both sides:
</span>
<span>
Divide both sides by -5/2 to get n by itself:
</span>
<span>
The value of n is 2.</span>
</span>
<span>
Subtract (2n + 3):
</span>
<span>
Your equation should now look like this:
</span>
<span>
Combine like terms on both sides:
</span>
<span>
Subtract 1/2n from both sides:
</span>
<span>
Divide both sides by -5/2 to get n by itself:
</span>
<span>
The value of n is 2.</span>
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.
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If a line is parallel to another line,Then the gradients are the same.So m=4 .Using general formula for str8 line, y=mx+c
sub in coorfinates (1,13)
So C=9.
sub in coorfinates (1,13)
So C=9.