Question

which equation shows the angle addition postulate?
\\(m\angle tsr + m\angle rsn = m\angle tsn\\)
\\(m\angle tsn + m\angle rsn = m\angle srt\\)
\\(m\angle tsn + m\angle rsn = m\angle tsr\\)
\\(m\angle tsn + m\angle rst = m\angle rsn\\)

\\(m\angle rsn = 37^\circ\\) and \\(m\angle rst = 172^\circ\\).
find \\(m\angle tsn\\).
first, substitute the known values.
\\(m\angle tsn + \\) \\(^\circ = \\) \\(^\circ\\)
next, solve for the unknown angle measure.
\\(m\angle tsn = \\) \\(^\circ\\)

Explanation:

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<reasoning>

Identify the adjacent angles

Using the Angle Addition Postulate knowledge point, we identify adjacent angles sharing a common ray.
Ray \(SN\) lies in the interior of \(\angle TSR\).
Therefore, \(\angle TSN\) and \(\angle RSN\) are adjacent angles.

Set up the addition equation

Using the Angle Addition Postulate knowledge point, the sum of the measures of adjacent angles equals the measure of the larger angle.
\[m\angle TSN + m\angle RSN = m\angle TSR\]
This matches the third multiple-choice option.

Substitute the given values

We are given \(m\angle RSN = 37^\circ\) and \(m\angle RST = 172^\circ\) (note that \(\angle RST\) is the same angle as \(\angle TSR\)).
Substitute these values into the postulate equation:
\[m\angle TSN + 37^\circ = 172^\circ\]

Solve for the unknown measure

Subtract \(37^\circ\) from both sides to find \(m\angle TSN\):
\[m\angle TSN = 172^\circ - 37^\circ = 135^\circ\]
</reasoning>

<answer>

Question 1

<mcq-option>(A) \(m\angle TSR + m\angle RSN = m\angle TSN\)</mcq-option>
<mcq-option>(B) \(m\angle TSN + m\angle RSN = m\angle SRT\)</mcq-option>
<mcq-correct>(C) \(m\angle TSN + m\angle RSN = m\angle TSR\)</mcq-correct>
<mcq-option>(D) \(m\angle TSN + m\angle RST = m\angle RSN\)</mcq-option>

Question 2

First, substitute the known values.
\(m\angle TSN +\) <blank>37</blank>\(^\circ =\) <blank>172</blank>\(^\circ\)

Question 3

Next, solve for the unknown angle measure.
\(m\angle TSN =\) <blank>135</blank>\(^\circ\)
</answer>

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Answer:

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<reasoning>

Identify the adjacent angles

Using the Angle Addition Postulate knowledge point, we identify adjacent angles sharing a common ray.
Ray \(SN\) lies in the interior of \(\angle TSR\).
Therefore, \(\angle TSN\) and \(\angle RSN\) are adjacent angles.

Set up the addition equation

Using the Angle Addition Postulate knowledge point, the sum of the measures of adjacent angles equals the measure of the larger angle.
\[m\angle TSN + m\angle RSN = m\angle TSR\]
This matches the third multiple-choice option.

Substitute the given values

We are given \(m\angle RSN = 37^\circ\) and \(m\angle RST = 172^\circ\) (note that \(\angle RST\) is the same angle as \(\angle TSR\)).
Substitute these values into the postulate equation:
\[m\angle TSN + 37^\circ = 172^\circ\]

Solve for the unknown measure

Subtract \(37^\circ\) from both sides to find \(m\angle TSN\):
\[m\angle TSN = 172^\circ - 37^\circ = 135^\circ\]
</reasoning>

<answer>

Question 1

<mcq-option>(A) \(m\angle TSR + m\angle RSN = m\angle TSN\)</mcq-option>
<mcq-option>(B) \(m\angle TSN + m\angle RSN = m\angle SRT\)</mcq-option>
<mcq-correct>(C) \(m\angle TSN + m\angle RSN = m\angle TSR\)</mcq-correct>
<mcq-option>(D) \(m\angle TSN + m\angle RST = m\angle RSN\)</mcq-option>

Question 2

First, substitute the known values.
\(m\angle TSN +\) <blank>37</blank>\(^\circ =\) <blank>172</blank>\(^\circ\)

Question 3

Next, solve for the unknown angle measure.
\(m\angle TSN =\) <blank>135</blank>\(^\circ\)
</answer>

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