Question

figure lmno is a parallelogram.
what is the value of (x)?
8
10
13
20

Explanation:

<pre_analysis>
{
"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",
"Solving Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Parallelogram Angle Properties",
"Solving Linear Equations"
]
}
</pre_analysis>

<reasoning>

Identify angle relationships

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &\angle M \text{ and } \angle N \text{ are consecutive interior angles.}\\ &m\angle M + m\angle N = 180^\circ \end{aligned}$$

\]

Set up the equation

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &(3x) + (8x - 40) = 180 \end{aligned}$$

\]

Solve for x

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &11x - 40 = 180\\ &11x = 220\\ &x = 20 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>8</mcq-option>
<mcq-option>10</mcq-option>
<mcq-option>13</mcq-option>
<mcq-correct>20</mcq-correct>
</answer>

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

Answer:

<pre_analysis>
{
"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",
"Solving Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Parallelogram Angle Properties",
"Solving Linear Equations"
]
}
</pre_analysis>

<reasoning>

Identify angle relationships

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &\angle M \text{ and } \angle N \text{ are consecutive interior angles.}\\ &m\angle M + m\angle N = 180^\circ \end{aligned}$$

\]

Set up the equation

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &(3x) + (8x - 40) = 180 \end{aligned}$$

\]

Solve for x

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &11x - 40 = 180\\ &11x = 220\\ &x = 20 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>8</mcq-option>
<mcq-option>10</mcq-option>
<mcq-option>13</mcq-option>
<mcq-correct>20</mcq-correct>
</answer>

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