rhombus lmno is shown with its diagonals.
angle mno measures $112^\circ$. what is the measure of angle lmn?
$34^\circ$
$56^\circ$
$68^\circ$

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rhombus Properties", "Consecutive Interior Angles" ], "new_concepts": [], "current_concepts": [ "Rhombus Properties", "Consecutive Interior Angles" ] } ## Identify the relationship between consecutive angles in a rhombus $$ \begin{aligned} &\text{Since a rhombus is a parallelogram, consecutive angles are supplementary:}\ &m\angle LMN + m\angle MNO = 180^\circ \end{aligned} $$ ## Substitute the given angle measure and solve $$ \begin{aligned} &m\angle MNO = 112^\circ\ &m\angle LMN + 112^\circ = 180^\circ\ &m\angle LMN = 180^\circ - 112^\circ\ &m\angle LMN = 68^\circ \end{aligned} $$

(A) $34^\circ$

(B) $56^\circ$

(C) $56^\circ$

(D) $68^\circ$

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

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Explanation:

Identify the relationship between consecutive angles in a rhombus

Substitute the given angle measure and solve

Answer: