Question

$\angle 1$ and $\angle 2$ are vertical angles. if $m\angle 1 = 17^{\circ}$ and $m\angle 2 = (x + 29)^{\circ}$, 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

We know \( m\angle1 = 17^\circ \) and \( m\angle2=(x + 29)^\circ \), so set up the equation: \( 17=x + 29 \).

Step3: Solve for \( x \)

Subtract 29 from both sides: \( x=17 - 29=- 12 \).

Answer:

\( x=-12 \)