Answered

IDNLearn.com: Your go-to resource for finding precise and accurate answers. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

What is the missing reason in step 3?

\begin{tabular}{|l|l|}
\hline
\textbf{Statements} & \textbf{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. \textbf{linear pair postulate} \\
4. [tex]$60 + 4x = 180$[/tex] & 4. substitution property of equality \\
5. [tex]$4x = 120$[/tex] & 5. subtraction property of equality \\
6. [tex]$x = 30$[/tex] & 6. division property of equality \\
\hline
\end{tabular}

A. substitution property of equality
B. angle addition postulate
C. subtraction property of equality
D. addition property of equality

Sagot :

GinnyAnsweridn
Certainly! Let's go through the step-by-step solution to understand the missing reason in step 3.

1. [tex]\( m \angle TRV = 60^\circ ; m \angle TRS = (4x)^\circ \)[/tex]
- Given: These angles and their expressions are provided in the problem statement.

2. [tex]\( \angle TRS \)[/tex] and [tex]\( \angle TRV \)[/tex] are a linear pair
- Reason: This statement is based on the definition of a linear pair. Linear pairs are pairs of adjacent angles formed when two lines intersect that are supplementary.

3. [tex]\( m \angle TRS + m \angle TRV = 180^\circ \)[/tex]
- Missing Reason: The measure of angles that form a linear pair are always supplementary (i.e., their measures add up to 180 degrees). This is based on the Linear Pair Postulate, which states that if two angles form a linear pair, then they are supplementary.

4. [tex]\( 60 + 4x = 180 \)[/tex]
- Reason: This follows from the substitution property of equality, where we replace [tex]\( m \angle TRV \)[/tex] with 60 and [tex]\( m \angle TRS \)[/tex] with [tex]\( 4x \)[/tex].

5. [tex]\( 4x = 120 \)[/tex]
- Reason: By applying the subtraction property of equality, we subtract 60 from both sides of the equation.

6. [tex]\( x = 30 \)[/tex]
- Reason: Finally, using the division property of equality, we divide both sides of the equation by 4 to solve for [tex]\( x \)[/tex].

So, the complete reasoning for step 3 is:

```
3. [tex]\( m \angle TRS + m \angle TRV = 180^\circ \)[/tex]
- Reason: Linear Pair Postulate
```
This postulate states that if two angles form a linear pair, their measures add up to 180 degrees.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Accurate answers are just a click away at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.