Question

given $m \parallel n$, find the value of $x$.

(image of two parallel lines m and n cut by a transversal t, creating angles $(x + 5)^\circ$ on line m and $(3x + 7)^\circ$ on line n)

answer attempt 1 out of 2

$x = \square$

Explanation:

Step1: Identify Angle Relationship

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (x + 5)^\circ \) and \( (3x + 7)^\circ \) are same - side interior angles. Same - side interior angles are supplementary, so their sum is \( 180^\circ \).
We can write the equation: \( (x + 5)+(3x + 7)=180 \)

Step2: Simplify the Equation

First, combine like terms: \( x+3x + 5+7=180 \)
\( 4x+12 = 180 \)

Step3: Solve for \( x \)

Subtract 12 from both sides: \( 4x=180 - 12=168 \)
Divide both sides by 4: \( x=\frac{168}{4}=42 \)

Answer:

\( x = 42 \)