Question

a quilt is designed using a square pattern. each square contains two rectangles. each rectangle contains a shaded rhombus.

what is the value of (x)?

50
55
125
145

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Properties of Quadrilaterals"
],
"new_concepts": [
"Rhombus Angle Properties"
],
"current_concepts": [
"Properties of Quadrilaterals",
"Rhombus Angle Properties"
]
}
</pre_analysis>

<reasoning>

Identify the relationship between consecutive angles of a rhombus

\[

$$\begin{aligned} &\text{Consecutive angles of a rhombus are supplementary:}\\ &50^\circ + (2x + 20)^\circ = 180^\circ \end{aligned}$$

\]

Solve the linear equation for x

\[

$$\begin{aligned} &2x + 70 = 180\\ &2x = 110\\ &x = 55 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>50</mcq-option>
<mcq-correct>55</mcq-correct>
<mcq-option>125</mcq-option>
<mcq-option>145</mcq-option>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Properties of Quadrilaterals"
],
"new_concepts": [
"Rhombus Angle Properties"
],
"current_concepts": [
"Properties of Quadrilaterals",
"Rhombus Angle Properties"
]
}
</pre_analysis>

<reasoning>

Identify the relationship between consecutive angles of a rhombus

\[

$$\begin{aligned} &\text{Consecutive angles of a rhombus are supplementary:}\\ &50^\circ + (2x + 20)^\circ = 180^\circ \end{aligned}$$

\]

Solve the linear equation for x

\[

$$\begin{aligned} &2x + 70 = 180\\ &2x = 110\\ &x = 55 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>50</mcq-option>
<mcq-correct>55</mcq-correct>
<mcq-option>125</mcq-option>
<mcq-option>145</mcq-option>
</answer>

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