What is the missing reason in step 3?

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

A. Substitution property of equality
B. Angle addition postulate
C. Subtraction property of equality
D. Addition property of equality

Question

17-06-2024
Mathematics

Answered

What is the missing reason in step 3?

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

A. Substitution property of equality
B. Angle addition postulate
C. Subtraction property of equality
D. Addition property of equality

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-17T10:48:28-04:00

To determine the correct reason for step 3, let's go through the logic step-by-step:

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

2. Definition of Linear Pair:
- [tex]\(\angle TRS\)[/tex] and [tex]\(\angle TRV\)[/tex] form a linear pair. By definition, a linear pair consists of two adjacent angles that form a straight line, summing up to 180°.

3. Step 3 Reasoning:
- For two angles forming a linear pair, the sum of their measures is 180°, because a straight angle is always equal to 180°.
- Therefore, the sum of [tex]\( m \angle TRS \)[/tex] and [tex]\( m \angle TRV \)[/tex] equals 180°.

The correct reasoning for this step is the angle addition postulate, which states that the measures of angles that form a linear pair add up to 180°.

So, the missing reason in step 3 is:

angle addition postulate