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{ "quality": "blurry", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Linear Equations" ], "new_concepts": [ "Triangle Exterior Angle Theorem", "Isosceles Triangle Theorem" ], "current_concepts": [ "Triangle Exterior Angle Theorem", "Isosceles Triangle Theorem", "Solving Linear Equations" ] } ## Apply the Exterior Angle Theorem to figure a $$ \begin{aligned} 30^\circ + x^\circ &= 100^\circ \ x &= 100 - 30 \ x &= 70 \end{aligned} $$ ## Apply the Exterior Angle Theorem to figure b $$ \begin{aligned} 2x^\circ + (3x + 2)^\circ &= 152^\circ \ 5x + 2 &= 152 \ 5x &= 150 \ x &= 30 \end{aligned} $$ ## Apply the Isosceles Triangle Theorem to figure c $$ \begin{aligned} (4x + 2)^\circ + 25^\circ + 25^\circ &= 180^\circ \ 4x + 52 &= 180 \ 4x &= 128 \ x &= 32 \end{aligned} $$ ## Question 6a $x = 70$ ## Question 6b $x = 30$ ## Question 6c $x = 32$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Properties" ] }

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Question

Explanation:

Apply the Exterior Angle Theorem to figure a

Apply the Exterior Angle Theorem to figure b

Apply the Isosceles Triangle Theorem to figure c

Answer:

Question 6a

Question 6b

Question 6c