Question

1. ( mangle 9 = (3x + 12)^circ )( mangle 10 = (x - 24)^circ )

Explanation:

Step1: Identify angle relationship

∠9 and ∠10 are supplementary (form a linear pair), so \( m\angle9 + m\angle10 = 180^\circ \).

Step2: Substitute angle expressions

Substitute \( m\angle9 = (3x + 12)^\circ \) and \( m\angle10 = (x - 24)^\circ \) into the equation:
\( (3x + 12) + (x - 24) = 180 \).

Step3: Simplify and solve for x

Combine like terms: \( 4x - 12 = 180 \).
Add 12 to both sides: \( 4x = 192 \).
Divide by 4: \( x = 48 \).

Answer:

\( x = 48 \)