Question

1. if ( m perp n ), solve for ( x ).

Explanation:

Step1: Recall perpendicular lines property

When two lines \( m \perp n \), the angles formed are right angles (\( 90^\circ \)). The two given angles \( (3x + 9)^\circ \) and \( (x + 21)^\circ \) should add up to \( 90^\circ \) because they are complementary (since \( m \) and \( n \) are perpendicular). So we set up the equation:
\( (3x + 9)+(x + 21)=90 \)

Step2: Simplify and solve for \( x \)

Combine like terms:
\( 3x + x+9 + 21 = 90 \)
\( 4x+30 = 90 \)

Subtract 30 from both sides:
\( 4x=90 - 30 \)
\( 4x = 60 \)

Divide both sides by 4:
\( x=\frac{60}{4} \)
\( x = 15 \)

Answer:

\( x = 15 \)