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What is the missing reason in step 3?

\begin{tabular}{ll|ll}
\multicolumn{1}{c|}{Statements} & \multicolumn{1}{c}{Reasons} \\
\hline
1. [tex]$m \angle TRV = 60^{\circ}; \ m \angle TRS = (4x)^{\circ}$[/tex] & 1. given \\
2. [tex]$\angle TRS$[/tex] and [tex]$\angle TRV$[/tex] are a linear pair & 2. definition of linear pair \\
3. [tex]$m \angle TRS + m \angle TRV = 180^{\circ}$[/tex] & 3. angle addition postulate \\
4. [tex]$60 + 4x = 180$[/tex] & 4. substitution \\
5. [tex]$4x = 120$[/tex] & 5. subtraction property of equality \\
6. [tex]$x = 30$[/tex] & 6. division property of equality \\
\end{tabular}

Choose the correct reason for step 3:
- angle addition postulate
- substitution property of equality
- subtraction property of equality
- addition property of equality



Answer :

GinnyAnswer
Sure, let's identify the missing reason in step 3.

Given that TRS and TRV are a linear pair, it means that the two angles together form a straight line.

Step-by-step solution:

1. Statement: [tex]\( m \angle TRV = 60^\circ ; m \angle TRS = (4x)^\circ \)[/tex]
- Reason: Given.

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

3. Statement: [tex]\( m \angle TRS + m \angle TRV = 180^\circ \)[/tex]
- Reason: Angle Addition Postulate. In a linear pair, the two angles add up to form a straight angle, which is [tex]\( 180^\circ \)[/tex].

4. Statement: [tex]\( 60 + 4x = 180 \)[/tex]
- Reason: Substitution of the given angle measures into the equation.

5. Statement: [tex]\( 4x = 120 \)[/tex]
- Reason: Subtraction Property of Equality. Subtracting 60 from both sides of the equation [tex]\( 60 + 4x = 180 \)[/tex].

6. Statement: [tex]\( x = 30 \)[/tex]
- Reason: Division Property of Equality. Dividing both sides of the equation [tex]\( 4x = 120 \)[/tex] by 4.

The missing reason in step 3 is Angle Addition Postulate.

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