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Sagot :
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
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
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