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:

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:

$$m\angle TSN = 172^\circ - 37^\circ = 135^\circ$$

Answer:

Question 1

Which equation shows the Angle Addition Postulate?

• o \(m\angle TSR + m\angle RSN = m\angle TSN\)
• o \(m\angle TSN + m\angle RSN = m\angle SRT\)
• • \(m\angle TSN + m\angle RSN = m\angle TSR\) (Correct answer)
• o \(m\angle TSN + m\angle RST = m\angle RSN\)

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>