Question

euclidean geometry
statements reasons
trv = 60°; 1. given
∠trs=(4x)°
∠trs and ∠trv are a linear 2. definition of linear pair
∠trs + m∠trv = 180 3. ?
60 + 4x = 180 4. substitution property of equality
4x = 120 5. subtraction property of equality
x = 30 6. division property of equality
given: m∠trv = 60°
∠trs=(4x)°
prove: x = 30
what is the missing reason in step 3?
substitution property of equality
angle addition postulate
addition property of equality
subtraction property of equality

Explanation:

Step1: Recall linear - pair property

If two angles form a linear pair, the sum of their measures is 180 degrees. This is based on the angle - addition postulate for adjacent angles that form a straight line.

Step2: Analyze step 3

Since $\angle TRS$ and $\angle TRV$ are a linear pair (from step 2), the reason for $\angle TRS + m\angle TRV=180$ is the angle addition postulate.

Answer:

angle addition postulate