Question

1. if m || n, solve for x.

(8x + 1)°
(21x + 5)°

Explanation:

Step1: Identify Angle Relationship

Since \( m \parallel n \), the angles \( (8x + 1)^\circ \) and \( (21x + 5)^\circ \) are same - side interior angles. Same - side interior angles are supplementary, so their sum is \( 180^\circ \).
We can write the equation: \( (8x + 1)+(21x + 5)=180 \)

Step2: Simplify the Equation

First, combine like terms on the left - hand side of the equation.
\( 8x+21x + 1 + 5=180 \)
\( 29x+6 = 180 \)

Step3: Solve for \( x \)

Subtract 6 from both sides of the equation:
\( 29x+6 - 6=180 - 6 \)
\( 29x=174 \)
Then divide both sides by 29:
\( x=\frac{174}{29} \)
\( x = 6 \)

Answer:

\( x = 6 \)