Given that mAngleKLH = 120° and mAngleKLM = 180°, which statement about the figure must be true?
AngleHLM is bisected by Ray L J .
AngleGLJ is bisected by Ray L H .
mAngleKLG = mAngleHLJ
mAngleHLI = mAngleILM
The correct statement is: AngleHLI = AngleILM
To determine which statement about the figure must be true, let's analyze the given information:
1. mAngleKLH = 120°: This tells us the measure of angle KLH is 120 degrees.
2. mAngleKLM = 180°: This tells us the measure of angle KLM is 180 degrees.
Now, let's evaluate each statement based on the given information:
1. AngleHLM is bisected by Ray L J: There is no information given about Ray L J. Therefore, we cannot conclude that angle HLM is bisected by Ray L J.
2. AngleGLJ is bisected by Ray L H: There is no information given about Ray L H. Therefore, we cannot conclude that angle GLJ is bisected by Ray L H.
3. mAngleKLG = mAngleHLJ: Since angle KLM is a straight line (180 degrees), angle KLG and angle HLJ are supplementary angles. However, without any information about their measures, we cannot determine if they are equal. Therefore, we cannot conclude that mAngleKLG = mAngleHLJ.
4. mAngleHLI = mAngleILM: Since angle KLM is a straight line (180 degrees), angle HLI and angle ILM are also supplementary angles. Again, without any information about their measures, we cannot determine if they are equal. Therefore, we cannot conclude that mAngleHLI = mAngleILM.
Based on the given information, none of the statements can be determined to be true.