Question

∠1 and ∠2 are vertical angles. if m∠1 = 3° and m∠2 = (2x + 9)°, then find the value of x.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).

Step2: Substitute given values

Substitute \( m\angle1 = 3^\circ \) and \( m\angle2=(2x + 9)^\circ \) into the equation: \( 3=2x + 9 \).

Step3: Solve for x

Subtract 9 from both sides: \( 3-9 = 2x+9 - 9 \), which simplifies to \( -6 = 2x \). Then divide both sides by 2: \( x=\frac{-6}{2}=-3 \).

Answer:

\( x = -3 \)