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What is the missing reason in step 3?

[tex]\[
\begin{array}{|c|c|}
\hline \text{Statements} & \text{Reasons} \\
\hline 1. m \angle \text{TRV} = 60^\circ ; m \angle \text{TRS} = (4x)^\circ & 1. \text{Given} \\
\hline 2. \angle \text{TRS} \text{ and } \angle \text{TRV} \text{ are a linear pair} & 2. \text{Definition of linear pair} \\
\hline 3. m \angle \text{TRS} + m \angle \text{TRV} = 180^\circ & 3. \text{Angle addition postulate} \\
\hline 4. 60 + 4x = 180 & 4. \text{Substitution property of equality} \\
\hline 5. 4x = 120 & 5. \text{Subtraction property of equality} \\
\hline 6. x = 30 & 6. \text{Division property of equality} \\
\hline
\end{array}
\][/tex]

- Substitution property of equality
- Angle addition postulate
- Subtraction property of equality
- Addition property of equality



Answer :

GinnyAnswer
Step 3 requires the principle that allows you to combine the measures of two angles that form a linear pair to sum up to 180 degrees. This principle is known as the "Angle Addition Postulate". According to the Angle Addition Postulate, if a point is in the interior of an angle, then the measure of the angle is the sum of the measures of the two angles formed.

Here is your detailed step-by-step solution:

1. Statements: [tex]\( m \angle TRV = 60^{\circ} \)[/tex]; [tex]\( m \angle TRS = (4x)^{\circ} \)[/tex]
Reasons: Given.

2. Statements: [tex]\( \angle TRS \)[/tex] and [tex]\( \angle TRV \)[/tex] are a linear pair.
Reasons: Definition of linear pair.

3. Statements: [tex]\( m \angle TRS + m \angle TRV = 180^{\circ} \)[/tex]
Reasons: Angle Addition Postulate.

4. Statements: [tex]\( 60 + 4x = 180 \)[/tex]
Reasons: Substitution property of equality.

5. Statements: [tex]\( 4x = 120 \)[/tex]
Reasons: Subtraction property of equality.

6. Statements: [tex]\( x = 30 \)[/tex]
Reasons: Division property of equality.

Therefore, the missing reason in step 3 is the Angle Addition Postulate.

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