Question

∠1 and ∠2 are vertical angles. if m∠1 = (3x + 22)° and m∠2 = (4x − 14)°, then find the value of x.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).
\[ 3x + 22 = 4x - 14 \]

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\[ 22 = x - 14 \]
Add 14 to both sides:
\[ x = 22 + 14 \]
\[ x = 36 \]

Answer:

\( 36 \)