Question

question given ( m parallel n ), find the value of ( x ). angles: ( (9x - 21)^circ ) and ( (8x - 3)^circ ) (from diagram)

Explanation:

Step1: Identify Alternate Interior Angles

Since \( m \parallel n \) and \( t \) is a transversal, \( (9x - 21)^\circ \) and \( (8x - 3)^\circ \) are alternate interior angles, so they are equal.
\[ 9x - 21 = 8x - 3 \]

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides:
\[ 9x - 8x - 21 = -3 \]
\[ x - 21 = -3 \]
Add 21 to both sides:
\[ x = -3 + 21 \]
\[ x = 18 \]

Answer:

\( x = 18 \)