in parallelogram lmno, what is the measure of angle m?

$20^\circ$
$60^\circ$
$80^\circ$
$100^\circ$

Question

in parallelogram lmno, what is the measure of angle m?

$20^\circ$
$60^\circ$
$80^\circ$
$100^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Properties of Quadrilaterals", "Parallelogram Definition" ], "new_concepts": [], "current_concepts": [ "Properties of Quadrilaterals", "Parallelogram Definition" ] } ## Set up the equation using consecutive interior angles $$ \begin{aligned} &m\angle L + m\angle N = 180^\circ \ &(3x + 40) + 5x = 180 \end{aligned} $$ ## Solve for x $$ \begin{aligned} &8x + 40 = 180 \ &8x = 140 \ &x = 17.5 \end{aligned} $$ ## Calculate the measure of angle M $$ \begin{aligned} &m\angle M = m\angle O = 180^\circ - m\angle L \ &m\angle L = 3(17.5) + 40 = 92.5^\circ \ &m\angle M = 180^\circ - 92.5^\circ = 87.5^\circ \quad (\text{Note: If opposite angles are equal, } m\angle M = m\angle O = 5x) \ &m\angle M = 5x = 5(17.5) = 87.5^\circ \end{aligned} $$ *(Self-correction: In a standard parallelogram labeled consecutively $L-M-N-O$, the consecutive vertices are $L, M, N, O$. Thus, $\angle L$ and $\angle N$ are opposite angles, meaning $m\angle L = m\angle N$. Let's re-evaluate:)* $$ \begin{aligned} &3x + 40 = 5x \ &2x = 40 \ &x = 20 \end{aligned} $$ $$ \begin{aligned} &m\angle L = m\angle N = 5(20) = 100^\circ \ &m\angle M = 180^\circ - m\angle L = 180^\circ - 100^\circ = 80^\circ \end{aligned} $$

(A) $20^\circ$

(B) $60^\circ$

(C) $80^\circ$

(D) $100^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Set up the equation using consecutive interior angles

Solve for x

Calculate the measure of angle M

Answer: