Question

which angles are corresponding angles?
∠hgj and ∠jdg
∠jdg and ∠kjg
∠ijl and ∠hgj
∠ijl and ∠fgj
diagram of lines and points: f, h; i, k; and transversal e, l with points g, j

Explanation:

To determine corresponding angles, we recall that corresponding angles are in the same relative position at each intersection where a transversal crosses two parallel lines. Let's analyze each option:

Step 1: Analyze ∠HGJ and ∠IDG

∠HGJ is at the intersection of transversal EL and line FH, while ∠IDG is not in a corresponding position relative to ∠HGJ. So this is not a pair of corresponding angles.

Step 2: Analyze ∠IDG and ∠KJG

∠IDG and ∠KJG: ∠KJG is at the intersection of transversal EL and line IK, but their positions don't match the definition of corresponding angles.

Step 3: Analyze ∠IJL and ∠HGJ

∠IJL is at the intersection of transversal EL and line IK, and ∠HGJ is at the intersection of transversal EL and line FH. These two angles are in the same relative position (both are above the transversal and to the left of their respective parallel lines), so they are corresponding angles.

Step 4: Analyze ∠IJL and ∠FGJ

∠IJL and ∠FGJ: Their positions do not align with the definition of corresponding angles.

Answer:

∠IJL and ∠HGJ (the option with ∠IJL and ∠HGJ)