e measure of angle a?

(10^{\circ})

(15^{\circ})

(90^{\circ})

(105^{\circ})

Question

e measure of angle a?

(10^{\circ})

(15^{\circ})

(90^{\circ})

(105^{\circ})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Triangle Angle Sum Theorem", "Right Triangle Properties" ], "current_concepts": [ "Triangle Angle Sum Theorem", "Right Triangle Properties" ] } ## Identify the given angles in right triangle ABC $$ \begin{aligned} &m\angle B = 90^\circ \ &m\angle C = 75^\circ \end{aligned} $$ ## Apply the Triangle Angle Sum Theorem $$ \begin{aligned} &m\angle A + m\angle B + m\angle C = 180^\circ \ &m\angle A + 90^\circ + 75^\circ = 180^\circ \end{aligned} $$ ## Solve for the measure of angle A $$ \begin{aligned} &m\angle A + 165^\circ = 180^\circ \ &m\angle A = 180^\circ - 165^\circ \ &m\angle A = 15^\circ \end{aligned} $$

(A) $10^\circ$

(B) $15^\circ$

(C) $90^\circ$

(D) $105^\circ$

{ "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 angles in right triangle ABC

Apply the Triangle Angle Sum Theorem

Solve for the measure of angle A

Answer: