given $m \\parallel n$, find the value of $x$.
given $m \\parallel n$, find the value of $x$.
Answer
Explanation:
Step1: Identify Alternate Interior Angles
Since ( m \parallel n ) and ( t ) is a transversal, the angles ( (3x - 15)^\circ ) and ( (x + 7)^\circ ) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So, we set up the equation:
( 3x - 15 = x + 7 )
Step2: Solve for ( x )
Subtract ( x ) from both sides:
( 3x - x - 15 = 7 )
( 2x - 15 = 7 )
Add 15 to both sides:
( 2x = 7 + 15 )
( 2x = 22 )
Divide both sides by 2:
( x = \frac{22}{2} )
( x = 11 )
Answer:
( x = 11 )