Solved on Dec 06, 2023

Given parallel lines $m$ and $n$ , find the relationship between the angles $(6x + 5)$ and $(5x - 12)$ and solve for $x$ .

STEP 1

Assumptions
1. Lines $m$ and $n$ are parallel.
2. The first angle is represented by the expression $(6x + 5)$ .
3. The second angle is represented by the expression $(5x - 12)$ .
4. The relationship between the two angles is not explicitly stated, but since the lines are parallel, we can assume they are either corresponding angles, alternate interior angles, or alternate exterior angles, which are all congruent.

STEP 2

Determine the relationship between the two angles. Since the lines are parallel and the angles are given by algebraic expressions, we can assume that the angles are either corresponding angles, alternate interior angles, or alternate exterior angles. In all these cases, the angles are congruent when the lines are cut by a transversal.
$\text{Angle } (6x + 5) \cong \text{Angle } (5x - 12)$

STEP 3

Set up an equation based on the congruency of the two angles.
$6x + 5 = 5x - 12$

STEP 4

Solve for $x$ by isolating the variable on one side of the equation. Start by subtracting $5x$ from both sides of the equation to get the $x$ terms on one side.
$6x + 5 - 5x = 5x - 12 - 5x$

STEP 5

Simplify the equation by combining like terms.
$x + 5 = -12$

STEP 6

Subtract 5 from both sides of the equation to isolate $x$ .
$x + 5 - 5 = -12 - 5$

STEP 7

Simplify the equation to find the value of $x$ .
$x = -12 - 5$ $x = -17$
The value of $x$ is $-17$ .

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Given parallel lines $m$ and $n$ , find the relationship between the angles $(6x + 5)$ and $(5x - 12)$ and solve for $x$ .

STEP 1

STEP 2

STEP 3

Set up an equation based on the congruency of the two angles.
$6x + 5 = 5x - 12$

STEP 4

Solve for $x$ by isolating the variable on one side of the equation. Start by subtracting $5x$ from both sides of the equation to get the $x$ terms on one side.
$6x + 5 - 5x = 5x - 12 - 5x$

STEP 5

Simplify the equation by combining like terms.
$x + 5 = -12$

STEP 6

Subtract 5 from both sides of the equation to isolate $x$ .
$x + 5 - 5 = -12 - 5$

STEP 7

Simplify the equation to find the value of $x$ .
$x = -12 - 5$ $x = -17$
The value of $x$ is $-17$ .

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Given parallel lines mmm and nnn, find the relationship between the angles (6x+5)(6x + 5)(6x+5) and (5x−12)(5x - 12)(5x−12) and solve for xxx.

STEP 1

STEP 2

STEP 3

Set up an equation based on the congruency of the two angles.6x+5=5x−126x + 5 = 5x - 126x+5=5x−12

STEP 4

Solve for xxx by isolating the variable on one side of the equation. Start by subtracting 5x5x5x from both sides of the equation to get the xxx terms on one side.6x+5−5x=5x−12−5x6x + 5 - 5x = 5x - 12 - 5x6x+5−5x=5x−12−5x

STEP 5

Simplify the equation by combining like terms.x+5=−12x + 5 = -12x+5=−12

STEP 6

Subtract 5 from both sides of the equation to isolate xxx.x+5−5=−12−5x + 5 - 5 = -12 - 5x+5−5=−12−5

STEP 7

Simplify the equation to find the value of xxx.x=−12−5x = -12 - 5x=−12−5 x=−17x = -17x=−17The value of xxx is −17-17−17.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Given parallel lines $m$ and $n$ , find the relationship between the angles $(6x + 5)$ and $(5x - 12)$ and solve for $x$ .

Set up an equation based on the congruency of the two angles.
$6x + 5 = 5x - 12$

Solve for $x$ by isolating the variable on one side of the equation. Start by subtracting $5x$ from both sides of the equation to get the $x$ terms on one side.
$6x + 5 - 5x = 5x - 12 - 5x$

Simplify the equation by combining like terms.
$x + 5 = -12$

Subtract 5 from both sides of the equation to isolate $x$ .
$x + 5 - 5 = -12 - 5$

Simplify the equation to find the value of $x$ .
$x = -12 - 5$ $x = -17$
The value of $x$ is $-17$ .