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Parallel Lines (Reasoning and Proof) Page 6 of 6
April 20
( 4 points) In the figure below,
m/_1=2x+10,m/_2=3x+30, and
m/_3=5x- Are lines
a and
b parallel? Show work and explain your reasoning.

2x+10

Parallel Lines (Reasoning and Proof) Page $6$ of $6$ $\newline$ April $20$ $\newline$ ( $4$ points) In the figure below, $m \angle 1=2 x+10, m \angle 2=3 x+30$ , and $m \angle 3=5 x-$ Are lines $a$ and $b$ parallel? Show work and explain your reasoning. $\newline$ $2 x+10$

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Add and subtract rational expressions

Full solution

Q. Parallel Lines (Reasoning and Proof) Page

6

of

6

\newline

April

20

\newline

(

4

points) In the figure below,

m \angle 1=2 x+10, m \angle 2=3 x+30

, and

m \angle 3=5 x-

Are lines

a

and

b

parallel? Show work and explain your reasoning.

\newline

2 x+10

Alternate Interior Angles Theorem: $m/_{1} = 2x + 10$ and $m/_{2} = 3x + 30$ are alternate interior angles, if lines $a$ and $b$ are parallel, then $m/_{1} = m/_{2}$ .
Set Equations Equal: Set the expressions for $m/_{1}$ and $m/_{2}$ equal to each other to solve for $x$ . $2x + 10 = 3x + 30$
Subtract $2x$ : Subtract $2x$ from both sides to get $x$ on one side. $\newline$ $10 = x + 30$
Subtract $30$ : Subtract $30$ from both sides to solve for $x$ . $\newline$ $-20 = x$

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