Question

what is the missing reason in step 3?

statements | reasons

1. m∠trv=60°, m∠trs=(4x)° | 1. given
2. ∠trs and ∠trv are a linear pair | 2. definition of linear pair
3. m∠trs + m∠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

options:

• substitution property of equality
• angle addition postulate
• subtraction property of equality
• addition property of equality

Explanation:

Step 3 states the sum of the measures of a linear pair equals 180°, which is the definition of supplementary angles (linear pairs are supplementary). The angle addition postulate applies when adding angles to form a larger angle, but here the key reason is that linear pair angles sum to 180°.

Answer:

angle addition postulate