triangle abc is an obtuse triangle with the obtuse angle at vertex b. angle a must be

less than 90°.
greater than 90°.
congruent to angle b.
congruent to angle c.

Question

triangle abc is an obtuse triangle with the obtuse angle at vertex b. angle a must be

less than 90°.
greater than 90°.
congruent to angle b.
congruent to angle c.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem" ], "new_concepts": [ "Obtuse Triangle Definition" ], "current_concepts": [ "Triangle Angle Sum Theorem", "Obtuse Triangle Definition" ] } ## Identify the given properties of the triangle $$ \begin{aligned} &\text{Triangle } ABC \text{ is obtuse with the obtuse angle at vertex } B.\ &m\angle B > 90^\circ \end{aligned} $$ ## Apply the angle sum theorem $$ \begin{aligned} &m\angle A + m\angle B + m\angle C = 180^\circ\ &m\angle A + m\angle C = 180^\circ - m\angle B \end{aligned} $$ ## Determine the range for angle A $$ \begin{aligned} &m\angle B > 90^\circ \implies 180^\circ - m\angle B < 90^\circ\ &m\angle A + m\angle C < 90^\circ\ &\text{Since } m\angle C > 0^\circ \implies m\angle A < 90^\circ \end{aligned} $$

less than 90°.

greater than 90°.

congruent to angle B.

congruent to angle C.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Angle Sum Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given properties of the triangle

Apply the angle sum theorem

Determine the range for angle A

Answer: