skill review 1

find the missing measurement of the parallelogram.

(a) 50^circ
(b) 90^circ
(c) 105^circ
(d) 130^circ

Question

skill review 1

find the missing measurement of the parallelogram.

(a) 50^circ
(b) 90^circ
(c) 105^circ
(d) 130^circ

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Parallelogram Properties", "Consecutive Interior Angles" ], "current_concepts": [ "Parallelogram Properties", "Consecutive Interior Angles" ] } ## Identify the geometric properties $$ \begin{aligned} &\text{Shape: Parallelogram } WXYZ\ &\text{Given angle: } \angle V = 75^\circ\ &\text{Target angle: } \angle W = ? \end{aligned} $$ ## Apply consecutive interior angles theorem $$ \begin{aligned} &\angle V + \angle W = 180^\circ\ &75^\circ + \angle W = 180^\circ \end{aligned} $$ ## Solve for the missing angle $$ \begin{aligned} &\angle W = 180^\circ - 75^\circ\ &\angle W = 105^\circ \end{aligned} $$

(A) $50^\circ$

(B) $90^\circ$

(C) $105^\circ$

(D) $130^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallelogram Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric properties

Apply consecutive interior angles theorem

Solve for the missing angle

Answer: