determine an expression for $x$ based on the following diagram:

diagram showing a triangle with an exterior angle. the interior angles are labeled as $x^\circ$ at the top and $7^\circ$ at the bottom-left. the exterior angle at the bottom-right is labeled as $4a - 1$.

$x = -2a + 8$
$x = 6a - 6$
$x = 2a - 8$
$x = 6a + 6$

Question

determine an expression for $x$ based on the following diagram:

diagram showing a triangle with an exterior angle. the interior angles are labeled as $x^\circ$ at the top and $7^\circ$ at the bottom-left. the exterior angle at the bottom-right is labeled as $4a - 1$.

$x = -2a + 8$
$x = 6a - 6$
$x = 2a - 8$
$x = 6a + 6$

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": [ "Exterior Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Exterior Angle Theorem", "Linear Equations" ] } ## Identify the given angles in the diagram Using the *Exterior Angle Theorem* knowledge point $$ \begin{aligned} &\text{Interior Angle 1: } 7\ &\text{Interior Angle 2: } x\ &\text{Exterior Angle: } 6a - 1 \end{aligned} $$ ## Set up the exterior angle equation Using the *Exterior Angle Theorem* knowledge point $$ \begin{aligned} &7 + x = 6a - 1 \end{aligned} $$ ## Solve for x Using the *Exterior Angle Theorem* knowledge point $$ \begin{aligned} &x = 6a - 1 - 7\ &x = 6a - 8 \end{aligned} $$

(A) $x = -2a + 8$

(B) $x = 6a - 6$ (C) $x = 2a - 8$

(D) $x = 6a + 6$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given angles in the diagram

Set up the exterior angle equation

Solve for x

Answer: