Question

∠1 and ∠2 are vertical angles. if m∠1 = (3x + 30)° and m∠2 = (8x − 30)°, then find the value of x.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).
\[ 3x + 30 = 8x - 30 \]

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\[ 30 = 5x - 30 \]
Add 30 to both sides:
\[ 60 = 5x \]
Divide both sides by 5:
\[ x = \frac{60}{5} = 12 \]

Answer:

\( 12 \)