Question

question given m || n, find the value of x. angles: (9x-21)°, (8x-3)° (diagram shows parallel lines m, n, transversal t)

Explanation:

Step1: Identify Alternate Interior Angles

Since \( m \parallel n \), the angles \( (9x - 21)^\circ \) and \( (6x - 3)^\circ \) are alternate interior angles, so they are equal.
\[ 9x - 21 = 6x - 3 \]

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\[ 9x - 6x - 21 = -3 \]
\[ 3x - 21 = -3 \]

Add 21 to both sides:
\[ 3x = -3 + 21 \]
\[ 3x = 18 \]

Divide by 3:
\[ x = \frac{18}{3} \]
\[ x = 6 \]

Answer:

\( x = 6 \)