the difference between the measures of two complementary angles is $42^{\circ}$. determine the measures of the two angles.

the larger angle has a measure of $\box^{\circ}$.
the smaller angle has a measure of $\box^{\circ}$.

Question

the difference between the measures of two complementary angles is $42^{\circ}$. determine the measures of the two angles.

the larger angle has a measure of $\box^{\circ}$.
the smaller angle has a measure of $\box^{\circ}$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Complementary Angles", "Systems of Linear Equations" ], "new_concepts": [], "current_concepts": [ "Complementary Angles", "Systems of Linear Equations" ] } ## Define variables for the two angles Let $x$ be the measure of the larger angle in degrees, and let $y$ be the measure of the smaller angle in degrees. ## Set up the system of equations Using the **Complementary Angles** and **Systems of Linear Equations** knowledge points $$ \begin{cases} x + y = 90 \ x - y = 42 \end{cases} $$ ## Solve the system of equations Using the **Systems of Linear Equations** knowledge point $$ \begin{aligned} (x + y) + (x - y) &= 90 + 42 \ 2x &= 132 \ x &= 66 \ y &= 90 - 66 = 24 \end{aligned} $$ The difference between the measures of two complementary angles is $42^{\circ}$. Determine the measures of the two angles. The larger angle has a measure of $66$$^{\circ}$. The smaller angle has a measure of $24$$^{\circ}$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Complementary Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Define variables for the two angles

Set up the system of equations

Solve the system of equations

Answer: