the difference between the measures of two complementary angles is $88^{\circ}$. determine the measures of the two angles.

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

Question

the difference between the measures of two complementary angles is $88^{\circ}$. determine the measures of the two angles.

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

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" ], "new_concepts": [ "Systems of Linear Equations" ], "current_concepts": [ "Complementary Angles", "Systems of Linear Equations" ] } ## Define the variables and system of equations Using the *Complementary Angles* knowledge point $$ \begin{aligned} &x + y = 90^\circ \ &x - y = 88^\circ \end{aligned} $$ ## Solve for the larger angle Using the *Complementary Angles* knowledge point $$ \begin{aligned} &(x + y) + (x - y) = 90^\circ + 88^\circ \ &2x = 178^\circ \ &x = 89^\circ \end{aligned} $$ ## Solve for the smaller angle Using the *Complementary Angles* knowledge point $$ \begin{aligned} &89^\circ + y = 90^\circ \ &y = 1^\circ \end{aligned} $$ The difference between the measures of two complementary angles is $88^\circ$. Determine the measures of the two angles. The larger angle has a measure of 89$^\circ$. The smaller angle has a measure of 1$^\circ$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Complementary Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Define the variables and system of equations

Solve for the larger angle

Solve for the smaller angle

Answer: