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Triangles do not have two obtuse angles.
J
Let's think about what we know about isosceles triangles. The name suggests that an isosceles triangle has two congruent sides. This also means that it has two congruent angles opposite to the congruent sides. Let's consider the different options presented in the question.
According to Corollary 4.2 to the Triangle Angle-Sum Theorem, a triangle cannot have two obtuse angles. Since it is given that angle ∠ A is obtuse, angle ∠ B cannot be obtuse. So, m∠ B is certainly not 94.
This however is impossible, because 94+47+47=188≠ 180. According to the Triangle Angle-Sum Theorem, these three angles are not angles of a triangle.
If AB=BC, then in the isosceles triangle △ ABC angles ∠ C and ∠ A are opposite to the congruent sides AB and BC, so these are congruent. ∠ C≅ ∠ A This is impossible, since it is given that ∠ A is obtuse, and a triangle cannot have two obtuse angles.
A triangle cannot have two obtuse angles. It is given that ∠ A is obtuse, so nether ∠ B nor ∠ C can be obtuse. ∠ B≠≅∠ A, ∠ C≠≅∠ A Since △ ABC is an isosceles triangle, it has two congruent angles. According to the previous observation, these two angles must be ∠ B and ∠ C. ∠ C≅∠ B In a triangle, sides opposite to congruent angles are congruent. AB≅AC Congruent segments have equal lengths, so option J is the correct answer.