Question

Given: (m angle TRV = 60^circ), (m angle TRS = (4x)^circ)

Prove: (x = 30)

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. angle sum property of a straight line
4. substitution property of equality
5. subtraction property of equality
6. division property of equality

Answer 1

The missing reason in step 3, which states that the measure of angles TRS and TRV add up to 180 degrees, is the angle sum property of a straight line. This is because the two angles are a linear pair, which by definition are adjacent angles that form a straight line when combined.

Step-by-step explanation:

The student has asked to prove that x = 30 given that the measure of angle TRV is 60 degrees and the measure of angle TRS is 4x degrees. Looking at the steps provided by the student, we can determine that the missing reason in step 3 is the angle sum property of a straight line, which states that the sum of angles that form a straight line is equal to 180 degrees. This property is used because angles TRS and TRV are a linear pair and thus their measures add up to 180 degrees.

1. Given: (m angle TRV = 60 degrees), (m angle TRS = (4x) degrees)
2. Angles TRS and TRV are a linear pair: Definition of a linear pair
3. (m angle TRS + m angle TRV = 180 degrees): Angle sum property of a straight line
4. 60 + 4x = 180: Substitution property of equality
5. 4x = 120: Subtraction property of equality
6. x = 30: Division property of equality