The given statement requires determining the relationship between angles 1, 4, and 7. Statement C holds true, while statements A, B, and D are not necessarily true.
If (
which of the following statements are true? Select all that apply.


Answer:
Only statement C is true.
Solution:
Statement A:
Angle 6 and angle 7 are not alternate interior angles, so we cannot conclude that they have the same measure. Therefore, statement A is not necessarily true.
Statement B:
Angle 5 and angle 7 are corresponding angles, but we cannot conclude that they have supplementary measures based on the information given. Therefore, statement B is not necessarily true.
Statement C:
Angles 1 and 4 are supplementary angles, so we can conclude that
However, we also know that
so we can conclude that
. Therefore,

Statement D:
Statement D is a transitive property statement, but it is not necessarily true based on the information given. For example, if angles 1 and 6 are not supplementary angles, then statement D would not be true. Therefore, statement D is not necessarily true.
Conclusion:
Only statement C is true.