1. The problem asks to identify which pairs of angles are vertical angles given two parallel lines FH and IK cut by a transversal. 2. Vertical angles are pairs of opposite angles formed when two lines intersect. They are equal in measure. 3. At point G, the transversal intersects line FH, creating angles including \(\angle HGJ\) and \(\angle FGJ\). 4. At point J, the transversal intersects line IK, creating angles including \(\angle IJG\), \(\angle JIL\), and \(\angle KJL\). 5. Vertical angles are formed at the same intersection point by opposite rays. So, vertical angles must share the same vertex. 6. Check each pair: - \(\angle HGJ\) and \(\angle FGJ\) share vertex G and are opposite angles, so they are vertical angles. - \(\angle HGJ\) and \(\angle KJL\) have different vertices (G and L), so not vertical angles. - \(\angle IJG\) and \(\angle JIL\) share vertex J but are adjacent, not opposite, so not vertical angles. - \(\angle HGJ\) and \(\angle FGE\) share vertex G but are adjacent, not opposite, so not vertical angles. 7. Therefore, the vertical angles are \(\angle HGJ\) and \(\angle FGJ\). Final answer: \(\angle HGJ\) and \(\angle FGJ\) are vertical angles.