angles c and d are complementary. the ratio of the measure of angle c to the measure of angle d is 2:3. what are the measures of both angles?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Proportional Relationships" ], "new_concepts": [ "Complementary Angles" ], "current_concepts": [ "Complementary Angles", "Proportional Relationships", "Linear Equations" ] } ## Define variables using the given ratio $$ \begin{aligned} &\text{Let } m\angle C = 2x \ &\text{Let } m\angle D = 3x \end{aligned} $$ ## Set up the equation using complementary angles $$ \begin{aligned} &2x + 3x = 90^\circ \ &5x = 90^\circ \ &x = 18^\circ \end{aligned} $$ ## Calculate the measure of each angle $$ \begin{aligned} &m\angle C = 2(18^\circ) = 36^\circ \ &m\angle D = 3(18^\circ) = 54^\circ \end{aligned} $$ $m\angle C = 36^\circ$ and $m\angle D = 54^\circ$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Complementary Angles" ] }

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Explanation:

Define variables using the given ratio

Set up the equation using complementary angles

Calculate the measure of each angle

Answer: