Question

which equation shows the angle addition postulate?

\\(m\angle tuy + m\angle yuv = m\angle tuv\\)
\\(m\angle tuy + m\angle uvy = m\angle tvu\\)
\\(m\angle ytu + m\angle yuv = m\angle tuv\\)
\\(m\angle tuy + m\angle tuv = m\angle yuv\\)

\\(m\angle tuy = 60^{\circ}\\) and \\(m\angle yuv = 71^{\circ}\\).
find \\(m\angle tuv\\).
\\(m\angle tuv =\\)

Explanation:

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<reasoning>

Identify the adjacent angles and the larger angle

\[

$$\begin{aligned} &\text{Adjacent angles: } \angle TUY \text{ and } \angle YUV\\ &\text{Larger angle: } \angle TUV \end{aligned}$$

\]

Apply the Angle Addition Postulate

\[
m\angle TUY + m\angle YUV = m\angle TUV
\]

Calculate the measure of the larger angle

\[

$$\begin{aligned} &m\angle TUY = 60^\circ\\ &m\angle YUV = 71^\circ\\ &m\angle TUV = 60^\circ + 71^\circ = 131^\circ \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

<mcq-correct>(A) m\angle TUY + m\angle YUV = m\angle TUV</mcq-correct>
<mcq-option>(B) m\angle TUY + m\angle UVY = m\angle TVU</mcq-option>
<mcq-option>(C) m\angle YTU + m\angle YUV = m\angle TUV</mcq-option>
<mcq-option>(D) m\angle TUY + m\angle TUV = m\angle YUV</mcq-option>

Question 2

The measure of the angle is <blank>131</blank> degrees.
</answer>

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"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Geometry",
"Angle Addition Postulate"
]
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</post_analysis>

Answer:

<pre_analysis>
{
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"question_count": 2,
"skills_matched": [
"step_cot",
"explain_then_answer",
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],
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"concepts_used": [
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],
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"current_concepts": [
"Angle Addition Postulate"
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</pre_analysis>

<reasoning>

Identify the adjacent angles and the larger angle

\[

$$\begin{aligned} &\text{Adjacent angles: } \angle TUY \text{ and } \angle YUV\\ &\text{Larger angle: } \angle TUV \end{aligned}$$

\]

Apply the Angle Addition Postulate

\[
m\angle TUY + m\angle YUV = m\angle TUV
\]

Calculate the measure of the larger angle

\[

$$\begin{aligned} &m\angle TUY = 60^\circ\\ &m\angle YUV = 71^\circ\\ &m\angle TUV = 60^\circ + 71^\circ = 131^\circ \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

<mcq-correct>(A) m\angle TUY + m\angle YUV = m\angle TUV</mcq-correct>
<mcq-option>(B) m\angle TUY + m\angle UVY = m\angle TVU</mcq-option>
<mcq-option>(C) m\angle YTU + m\angle YUV = m\angle TUV</mcq-option>
<mcq-option>(D) m\angle TUY + m\angle TUV = m\angle YUV</mcq-option>

Question 2

The measure of the angle is <blank>131</blank> degrees.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Geometry",
"Angle Addition Postulate"
]
}
</post_analysis>