Question

what is the value of j?

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. The angle adjacent to the given $59.9^{\circ}$ angle and angle $j$ are vertical angles.

Step2: Use the linear - pair property

The sum of adjacent angles forming a straight - line is $180^{\circ}$. Let the adjacent angle to $59.9^{\circ}$ be $x$. So $x + 59.9^{\circ}=180^{\circ}$, then $x = 180^{\circ}-59.9^{\circ}=120.1^{\circ}$.
Since $j$ and $x$ are vertical angles, $j=x$.

Answer:

$120.1^{\circ}$