question 4 of 10

given \square abcd, what is the measure of \angle b?

a. 90^{\circ}
b. 235^{\circ}
c. 145^{\circ}
d. 35^{\circ}
e. 10^{\circ}
f. 55^{\circ}

Question

question 4 of 10

given \square abcd, what is the measure of \angle b?

a. 90^{\circ}
b. 235^{\circ}
c. 145^{\circ}
d. 35^{\circ}
e. 10^{\circ}
f. 55^{\circ}

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": [ "Parallelogram Angle Properties", "Consecutive Interior Angles" ], "new_concepts": [], "current_concepts": [ "Parallelogram Angle Properties", "Consecutive Interior Angles" ] } ## Identify the given geometric properties Using the *Parallelogram Angle Properties* knowledge point $$ \begin{aligned} &\text{Given: } \square ABCD \text{ is a parallelogram.}\ &m\angle D = 145^\circ \end{aligned} $$ ## Apply consecutive interior angles relationship Using the *Consecutive Interior Angles* knowledge point $$ \begin{aligned} &AD \parallel BC \implies m\angle D + m\angle C = 180^\circ\ &AB \parallel CD \implies m\angle D + m\angle A = 180^\circ \end{aligned} $$ ## Apply opposite angles relationship Using the *Parallelogram Angle Properties* knowledge point $$ \begin{aligned} &m\angle B = m\angle D \quad \text{(Opposite angles are congruent)}\ &m\angle B = 145^\circ \end{aligned} $$

A. $90^\circ$

B. $235^\circ$

C. $145^\circ$

D. $35^\circ$

E. $10^\circ$

F. $55^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric properties

Apply consecutive interior angles relationship

Apply opposite angles relationship

Answer: