Question

find \\(m\angle efy\\) if \\(m\angle efg = 74^{\circ}\\) and \\(m\angle yfg = 20^{\circ}\\)

\\(m\angle efy =\\)

Explanation:

<pre_analysis>
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"concepts_used": [],
"new_concepts": [
"Angle Addition Postulate"
],
"current_concepts": [
"Angle Addition Postulate",
"Rays and Segments"
]
}
</pre_analysis>

<reasoning>

Identify the given angle measures

\[

$$\begin{aligned} m\angle EFG &= 74^\circ \\ m\angle YFG &= 20^\circ \end{aligned}$$

\]

Apply the Angle Addition Postulate

\[

$$\begin{aligned} m\angle EFY + m\angle YFG &= m\angle EFG \\ m\angle EFY + 20^\circ &= 74^\circ \end{aligned}$$

\]

Solve for the unknown angle

\[

$$\begin{aligned} m\angle EFY &= 74^\circ - 20^\circ \\ m\angle EFY &= 54^\circ \end{aligned}$$

\]
</reasoning>

<answer>
Find \(m\angle EFY\) if \(m\angle EFG = 74^\circ\) and \(m\angle YFG = 20^\circ\).

\(m\angle EFY =\) <blank>\(54^\circ\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Angle Addition Postulate"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
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"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Angle Addition Postulate"
],
"current_concepts": [
"Angle Addition Postulate",
"Rays and Segments"
]
}
</pre_analysis>

<reasoning>

Identify the given angle measures

\[

$$\begin{aligned} m\angle EFG &= 74^\circ \\ m\angle YFG &= 20^\circ \end{aligned}$$

\]

Apply the Angle Addition Postulate

\[

$$\begin{aligned} m\angle EFY + m\angle YFG &= m\angle EFG \\ m\angle EFY + 20^\circ &= 74^\circ \end{aligned}$$

\]

Solve for the unknown angle

\[

$$\begin{aligned} m\angle EFY &= 74^\circ - 20^\circ \\ m\angle EFY &= 54^\circ \end{aligned}$$

\]
</reasoning>

<answer>
Find \(m\angle EFY\) if \(m\angle EFG = 74^\circ\) and \(m\angle YFG = 20^\circ\).

\(m\angle EFY =\) <blank>\(54^\circ\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Angle Addition Postulate"
]
}
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