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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Proofs", "Linear Pair", "Postulates and Axioms" ], "new_concepts": [ "Exterior Angle Theorem Proof", "Triangle Angle Sum Theorem" ], "current_concepts": [ "Geometric Proofs", "Linear Pair", "Postulates and Axioms", "Exterior Angle Theorem Proof", "Triangle Angle Sum Theorem" ] } ## Identify the given statements and reasons $$ \begin{aligned} &\text{Statement 1: } m\angle DCA + m\angle ACB = 180^\circ \quad \text{(Reason: Linear Pair Postulate)} \ &\text{Statement 2: } m\angle B + m\angle ACB + m\angle A = 180^\circ \quad \text{(Reason: Triangle Angle Sum Theorem)} \ &\text{Statement 3: } m\angle DCA + m\angle ACB = m\angle B + m\angle ACB + m\angle A \quad \text{(Reason: Substitution)} \ &\text{Statement 4: } m\angle DCA = m\angle B + m\angle A \quad \text{(Reason: Subtraction Property of Equality)} \end{aligned} $$ ## Map the flow chart elements $$ \begin{aligned} &\text{Top Left Box: } m\angle DCA + m\angle ACB = 180^\circ \ &\text{Top Left Reason: Linear Pair Postulate} \ &\text{Top Right Box: } m\angle B + m\angle ACB + m\angle A = 180^\circ \ &\text{Top Right Reason: Triangle Angle Sum Theorem} \ &\text{Middle Box: } m\angle DCA + m\angle ACB = m\angle B + m\angle ACB + m\angle A \ &\text{Middle Reason: Substitution} \ &\text{Bottom Box: } m\angle DCA = m\angle B + m\angle A \ &\text{Bottom Reason: Subtraction} \end{aligned} $$ Based on the paragraph and the drag-and-drop options at the bottom of the screen, the completed flow proof for the Exterior Angle Theorem is: - **Top Left Statement:** $m\angle DCA + m\angle ACB = 180^\circ$ - **Top Left Reason:** Linear Pair Postulate - **Top Right Statement:** $m\angle B + m\angle ACB + m\angle A = 180^\circ$ - **Top Right Reason:** Triangle Angle Sum Theorem - **Middle Statement:** $m\angle DCA + m\angle ACB = m\angle B + m\angle ACB + m\angle A$ - **Middle Reason:** Substitution - **Bottom Statement:** $m\angle DCA = m\angle B + m\angle A$ - **Bottom Reason:** Subtraction { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Proofs" ] }

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Explanation:

Identify the given statements and reasons

Map the flow chart elements

Answer: