determine an expression for $x$ and $y$ in terms of $a$ based on the following diagram:

diagram showing a triangle with interior angles $14a + 1$, $5a + 3$, and $6a - 2$. the exterior angles adjacent to $5a + 3$ and $6a - 2$ are labeled $x$ and $y$ respectively.

$x = 20a - 1$ and $y = 19a + 4$
$x = 19a + 4$ and $y = 20a - 1$
$x = 11a + 1$ and $y = -a - 5$
$x = -11a + 1$ and $y = a - 5$

Question

determine an expression for $x$ and $y$ in terms of $a$ based on the following diagram:

diagram showing a triangle with interior angles $14a + 1$, $5a + 3$, and $6a - 2$. the exterior angles adjacent to $5a + 3$ and $6a - 2$ are labeled $x$ and $y$ respectively.

$x = 20a - 1$ and $y = 19a + 4$
$x = 19a + 4$ and $y = 20a - 1$
$x = 11a + 1$ and $y = -a - 5$
$x = -11a + 1$ and $y = a - 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Supplementary Angles", "Exterior Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Supplementary Angles", "Exterior Angle Theorem" ] } ## Find the value of a Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} (14a + 1) + (5a + 3) + (6a - 2) &= 180 \ 25a + 2 &= 180 \ 25a &= 178 \ a &= 7.12 \end{aligned} $$ ## Express x in terms of a Using the *Exterior Angle Theorem* knowledge point $$ \begin{aligned} x &= (14a + 1) + (6a - 2) \ x &= 20a - 1 \end{aligned} $$ ## Express y in terms of a Using the *Exterior Angle Theorem* knowledge point $$ \begin{aligned} y &= (14a + 1) + (5a + 3) \ y &= 19a + 4 \end{aligned} $$ ## Verify with supplementary angles Using the *Supplementary Angles* knowledge point $$ \begin{aligned} x + (5a + 3) &= (20a - 1) + (5a + 3) = 25a + 2 = 180 \ y + (6a - 2) &= (19a + 4) + (6a - 2) = 25a + 2 = 180 \end{aligned} $$

(A) $x = 20a - 1$ and $y = 19a + 4$

(B) $x = 19a + 4$ and $y = 20a - 1$

(C) $x = 11a + 1$ and $y = -a - 5$

(D) $x = -11a + 1$ and $y = a - 5$

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

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QUESTION IMAGE

Question

Explanation:

Find the value of a

Express x in terms of a

Express y in terms of a

Verify with supplementary angles

Answer: