Question

assume lines p and q intersect to form adjacent angles 1 and 2. if m∠1 = (7x + 6)° and m∠2 = (8x − 6)°, find the value of x such that p is perpendicular to q. x=

Explanation:

Step1: Recall perpendicular lines property

If lines \( p \) and \( q \) are perpendicular, adjacent angles formed by their intersection are right angles (sum to \( 90^\circ \)). So, \( m\angle1 + m\angle2 = 90^\circ \).

Step2: Substitute angle expressions

Substitute \( m\angle1=(7x + 6)^\circ \) and \( m\angle2=(8x - 6)^\circ \) into the equation:
\( (7x + 6)+(8x - 6)=90 \)

Step3: Simplify and solve for \( x \)

Combine like terms: \( 7x + 8x + 6 - 6 = 90 \)
\( 15x = 90 \)
Divide both sides by 15: \( x=\frac{90}{15}=6 \)

Answer:

\( 6 \)