Question

what is the missing reason in step 3?

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

Explanation:

Step1: Recall linear pair property

If two angles form a linear pair, their measures add up to \(180^{\circ}\).

Step2: Apply to the problem

Since \(\angle TRS\) and \(\angle TRV\) are a linear pair (from step 2), by the linear pair postulate (which states that if two angles form a linear pair, then the sum of their measures is \(180^{\circ}\)), we have \(m\angle TRS + m\angle TRV=180\).

Answer:

linear pair postulate