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 = \\)

Explanation:

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<reasoning>

Identify the correct Angle Addition Postulate equation

The diagram shows adjacent angles \(\angle TSN\) and \(\angle RSN\) sharing the common ray \(\vec{SN}\) inside the larger angle \(\angle TSR\) (also named \(\angle RST\)).
Therefore, the sum of the measures of the two adjacent angles equals the measure of the larger angle:
\[m\angle TSN + m\angle RSN = m\angle TSR\]

Substitute the known values

Given values:
\[m\angle RSN = 37^\circ\]
\[m\angle RST = 172^\circ \quad (\text{which is } m\angle TSR)\]
Substituting these values into the equation:
\[m\angle TSN + 37^\circ = 172^\circ\]

Solve for the unknown angle measure

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

<answer>

Question 1

Which equation shows the Angle Addition Postulate?
<mcq-option>o \(m\angle TSR + m\angle RSN = m\angle TSN\)</mcq-option>
<mcq-option>o \(m\angle TSN + m\angle RSN = m\angle SRT\)</mcq-option>
<mcq-correct>• \(m\angle TSN + m\angle RSN = m\angle TSR\)</mcq-correct>
<mcq-option>o \(m\angle TSN + m\angle RST = m\angle RSN\)</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>
</answer>

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Answer:

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<reasoning>

Identify the correct Angle Addition Postulate equation

The diagram shows adjacent angles \(\angle TSN\) and \(\angle RSN\) sharing the common ray \(\vec{SN}\) inside the larger angle \(\angle TSR\) (also named \(\angle RST\)).
Therefore, the sum of the measures of the two adjacent angles equals the measure of the larger angle:
\[m\angle TSN + m\angle RSN = m\angle TSR\]

Substitute the known values

Given values:
\[m\angle RSN = 37^\circ\]
\[m\angle RST = 172^\circ \quad (\text{which is } m\angle TSR)\]
Substituting these values into the equation:
\[m\angle TSN + 37^\circ = 172^\circ\]

Solve for the unknown angle measure

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

<answer>

Question 1

Which equation shows the Angle Addition Postulate?
<mcq-option>o \(m\angle TSR + m\angle RSN = m\angle TSN\)</mcq-option>
<mcq-option>o \(m\angle TSN + m\angle RSN = m\angle SRT\)</mcq-option>
<mcq-correct>• \(m\angle TSN + m\angle RSN = m\angle TSR\)</mcq-correct>
<mcq-option>o \(m\angle TSN + m\angle RST = m\angle RSN\)</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>
</answer>

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