Question

what is the missing reason in step 3?
statements

1. $m\angle trv=60^\circ$; $m\angle trs=(4x)^\circ$
2. $\angle trs$ and $\angle trv$ are a linear pair
3. $m\angle trs + m\angle trv = 180$
4. $60+4x=180$
5. $4x = 120$
6. $x=30$

reasons

1. given
2. definition of linear pair
3. ?
4. substitution property of equality
5. subtraction property of equality
6. division property of equality

$circ$ substitution property of equality
$circ$ angle addition postulate
$circ$ subtraction property of equality
$circ$ addition property of equality

Explanation:

Step 3 states that the sum of the measures of a linear pair of angles is 180°. This comes from the angle addition postulate, which defines that two adjacent angles forming a linear pair combine to form a straight angle (180°). The other options do not fit: substitution replaces values, subtraction/equality properties modify equations, not define angle sums for linear pairs.

Answer:

angle addition postulate