Question

$\angle 1$ and $\angle 2$ are vertical angles. if $m\angle 1 = (7x - 9)^{circ}$ and $m\angle 2 = (6x + 11)^{circ}$, then find the value of $x$.

Explanation:

Step1: Recall vertical angles property

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

Step2: Set up the equation

Substitute the given expressions: \( 7x - 9 = 6x + 11 \).

Step3: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 7x - 6x - 9 = 6x - 6x + 11 \), which simplifies to \( x - 9 = 11 \). Then add 9 to both sides: \( x - 9 + 9 = 11 + 9 \), so \( x = 20 \).

Answer:

\( x = 20 \)