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Answer:
E
Step-by-step explanation:
A. The ⊥ symbol means "is perpendicular to". The two lines l1 and l2 are parallel, not perpendicular.
B. Angles g and f are vertical angles. They are congruent. If both are 45°, then they are complementary, but we cannot assume that is the case. They are shown as obtuse angles.
C. Angles e and h are vertical angles. They are congruent. If both are 45°, then they are complementary, but we cannot assume that is the case. They are shown as acute angles, but with no particular angle measure.
D. Angle d is shown as an acute angle. In general, we cannot assume its measure based on its appearance in the diagram.
E. Angles d and g are shown as, respectively, an acute angle and an obtuse angle. Where a transversal crosses parallel lines, all acute angles are supplementary to all obtuse angles. Hence the sum of angles d and g will be 180 degrees. This statement is true.
F. Angles c and f are congruent angles, shown as obtuse. Their sum will be 270° if and only if their measures are each 135°. There is no indication in the diagram that the angles have any particular measure, so we cannot assume their sum is 270°.
