Her proof is not correct because angles ∠B and ∠C are complementary, not supplementary.
What angles are not supplementary?
If you add two acute angles in which each angle is large as possible, its sum will be less than 180°. By the definition of supplementary angles, it is impossible to get the supplementary angle when we add two acute angles.
How do you know if angles are complementary neither or supplementary?
Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. Supplementary and complementary angles do not have to be adjacent, but they can be.
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