To analyze the given angles, let's summarize the information provided:
- \( m\angle KLH = 120^\circ \)
- \( m\angle KLM = 180^\circ \)
From this, we can derive \( m\angle HLM \) as follows:
-
Since \( m\angle KLM = 180^\circ \), this means that points K, L, and M are collinear and points K and M lie on opposite sides of point L.
-
Now, \( m\angle KLH = 120^\circ \) implies that angle H is on the opposite side of line KM when compared to angle KLM.
-
Knowing that angles around a point sum up to \( 360^\circ \), we can determine \( m\angle HLM \): \[ m\angle HLM + m\angle KLH + m\angle KLM = 360^\circ \] Substituting the known values: \[ m\angle HLM + 120^\circ + 180^\circ = 360^\circ \] \[ m\angle HLM + 300^\circ = 360^\circ \] \[ m\angle HLM = 60^\circ \]
Now let's analyze the given statements one by one to see which must be true:
-
Angle HLM is bisected by Ray LJ: This cannot be concluded solely from the given information; no information regarding Ray LJ or the relationship to angle HLM is provided.
-
Angle GLJ is bisected by Ray LH: There is no information given about angle GLJ or Ray LH. Therefore, we cannot verify this statement as true.
-
mAngle KLG = mAngle HLJ: We have no specific values or relationships between angles KLG and HLJ based on the information provided.
-
mAngle HLI = mAngle ILM: Again, we lack specific values or relationships between angles HLI and ILM from what has been provided.
Therefore, based on the statements and analysis, none of the conclusions can be reached definitively with the given information. If one conclusion must be chosen, it is that:
None of the statements must necessarily be true based solely on the information provided.