Question

what is the missing reason in step 3? statements reasons 1. (mangle trv = 60^{circ};mangle trs=(4x)^{circ}) 1. given 2. (angle trs) and (angle trv) are a linear pair 2. definition of linear pair 3. (mangle trs + mangle trv=180) 3. ? 4. (60 + 4x=180) 4. substitution property of equality 5. (4x = 120) 5. subtraction property of equality 6. (x = 30) 6. division property of equality substitution property of equality angle addition postulate subtraction property of equality addition property of equality

Explanation:

Step1: Recall angle - related postulates

Linear pairs of angles are adjacent angles that form a straight - line. By the angle addition postulate, the sum of the measures of angles in a linear pair is 180 degrees.

Step2: Analyze the step

In step 3, we go from the fact that $\angle TRS$ and $\angle TRV$ are a linear pair (step 2) to $m\angle TRS + m\angle TRV=180$. This is based on the angle addition postulate which states that if two angles form a linear pair, the sum of their measures is 180 degrees.

Answer:

angle addition postulate