What is the missing reason in step 3?Statements:1. m∠ TRV=60° m∠ TRS=(4x)^circ 2. ∠ TRS and ∠ TRV are a linear pair 3. m∠ TRS+m∠ TRV=180 4. 60+4x=180 5. 4x=120 6. x=30Reasons:1. given 2. definition of linear pair 3.? 4.substitution property of equality 5.subtraction property of equality 6. division property of equality substitution property of equalityangle addition postulatesubtraction property of equalityaddition property of equality

To find the missing reason for step 3:

1. Identify the step: \(m∠ TRS + m∠ TRV = 180° \).
2. Recognize that this step follows from the definition of a linear pair.
3. The angle addition postulate states that the sum of the measures of adjacent angles forming a straight line is 180°.
4. Therefore, the missing reason is the angle addition postulate.

Supplemental Knowledge

In geometry, understanding the relationships between angles is fundamental. Here are some key concepts that are relevant to this problem:

1. Linear Pair:
   • A linear pair of angles is formed when two adjacent angles add up to 180 degrees. This relationship is crucial in many geometric proofs and problems.
2. Angle Addition Postulate:
   • This postulate states that if a point lies on the interior of an angle, the sum of the measures of the two smaller angles created equals the measure of the original angle.
3. Properties of Equality:
   • These properties include substitution, addition, subtraction, multiplication, and division properties, which are used to manipulate equations and solve for unknowns in geometric proofs.

Life in Context

Imagine you're designing a piece of furniture and want to ensure certain parts fit together at precise angles. By knowing that adjacent parts forming a straight line must add up to 180 degrees (a linear pair), it becomes much simpler and accurate for measuring required measurements accurately. For instance, if one part forms an angle with another of 60 degrees then its complementary part should form 120-degree angles to complete this pair linear pair.

For students tackling challenging geometry problems like these, UpStudy offers invaluable resources! Our live tutor question bank and AI-powered problem-solving services provide detailed explanations and step-by-step guidance on complex topics.
To further assist with your geometry problems and proofs, try using UpStudy's Geometry Calculator! It’s perfect for helping you understand complex concepts and solve challenging questions with ease.