Question

yolanda is making a banner for a school pep rally. she cuts fabric in the shape of a parallelogram. the angle at the bottom-left corner measures \\(80^{\circ}\\).

what is the value of \\(x\\)?

40
50
100
160

Explanation:

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<reasoning>

Identify the given geometric properties

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &\text{Shape: Parallelogram}\\ &\angle_{\text{bottom-left}} = 80^\circ\\ &\angle_{\text{top-left}} = x^\circ \end{aligned}$$

\]

Apply consecutive interior angles theorem

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &x + 80 = 180\\ &x = 100 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 40</mcq-option>
<mcq-option>(B) 50</mcq-option>
<mcq-correct>(C) 100</mcq-correct>
<mcq-option>(D) 160</mcq-option>
</answer>

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

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}
</pre_analysis>

<reasoning>

Identify the given geometric properties

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &\text{Shape: Parallelogram}\\ &\angle_{\text{bottom-left}} = 80^\circ\\ &\angle_{\text{top-left}} = x^\circ \end{aligned}$$

\]

Apply consecutive interior angles theorem

Using the Parallelogram Angle Properties knowledge point
\[

$$\begin{aligned} &x + 80 = 180\\ &x = 100 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 40</mcq-option>
<mcq-option>(B) 50</mcq-option>
<mcq-correct>(C) 100</mcq-correct>
<mcq-option>(D) 160</mcq-option>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
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