Question

right trapezoid wxyz is shown.
what is the measure of angle wxy?

73^
90^
107^
163^

Explanation:

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"concepts_used": [
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"Quadrilateral Angle Sum"
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"new_concepts": [
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</pre_analysis>

<reasoning>

Identify the given properties of the trapezoid

Using the Trapezoid Properties knowledge point
\[

$$\begin{aligned} &XY \parallel WZ\\ &m\angle Y = 90^\circ\\ &m\angle Z = 90^\circ\\ &m\angle W = 73^\circ \end{aligned}$$

\]

Calculate the measure of angle WXY

Using the Quadrilateral Angle Sum knowledge point
\[

$$\begin{aligned} &m\angle W + m\angle X + m\angle Y + m\angle Z = 360^\circ\\ &73^\circ + m\angle WXY + 90^\circ + 90^\circ = 360^\circ\\ &m\angle WXY + 253^\circ = 360^\circ\\ &m\angle WXY = 360^\circ - 253^\circ = 107^\circ \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(73^\circ\)</mcq-option>
<mcq-option>(B) \(90^\circ\)</mcq-option>
<mcq-correct>(C) \(107^\circ\)</mcq-correct>
<mcq-option>(D) \(163^\circ\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
"Geometry",
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</post_analysis>

Answer:

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"Quadrilateral Angle Sum",
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</pre_analysis>

<reasoning>

Identify the given properties of the trapezoid

Using the Trapezoid Properties knowledge point
\[

$$\begin{aligned} &XY \parallel WZ\\ &m\angle Y = 90^\circ\\ &m\angle Z = 90^\circ\\ &m\angle W = 73^\circ \end{aligned}$$

\]

Calculate the measure of angle WXY

Using the Quadrilateral Angle Sum knowledge point
\[

$$\begin{aligned} &m\angle W + m\angle X + m\angle Y + m\angle Z = 360^\circ\\ &73^\circ + m\angle WXY + 90^\circ + 90^\circ = 360^\circ\\ &m\angle WXY + 253^\circ = 360^\circ\\ &m\angle WXY = 360^\circ - 253^\circ = 107^\circ \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(73^\circ\)</mcq-option>
<mcq-option>(B) \(90^\circ\)</mcq-option>
<mcq-correct>(C) \(107^\circ\)</mcq-correct>
<mcq-option>(D) \(163^\circ\)</mcq-option>
</answer>

<post_analysis>
{
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Trapezoid Properties"
]
}
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