Question

drag the missing reason for step 4 to the box.

statements | reasons

1. ( mangle elk = 130^circ ); ( mangle elf = (10x)^circ ) | 1. given
2. ( angle elk ) and ( angle elf ) are a linear pair. | 2. definition of linear pair
3. ( mangle elk + mangle elf = 180^circ ) | 3. angle addition postulate
4. ( 130 + 10x = 180 ) | 4. missing
5. ( 10x = 50 ) | 5. subtraction property of equality
6. ( x = 5 ) | 6. division property of equality

options: substitution property of equality, addition property of equality, vertical angles postulate, triangle sum property

Explanation:

Step1: Analyze Step 4

We know from Step 1 that \( m\angle ELK = 130^\circ \) and \( m\angle ELF=(10x)^\circ \), and from Step 3 we have \( m\angle ELK + m\angle ELF = 180^\circ \). In Step 4, we substitute the values of \( m\angle ELK \) and \( m\angle ELF \) into the equation from Step 3.

Step2: Identify the Property

The substitution property of equality states that if \( a = b \), then \( a \) can be substituted for \( b \) (or vice versa) in any equation or expression. Here, we substitute \( 130 \) for \( m\angle ELK \) and \( 10x \) for \( m\angle ELF \) in the equation \( m\angle ELK + m\angle ELF = 180^\circ \) to get \( 130 + 10x = 180 \). So the reason for Step 4 is the substitution property of equality.

Answer:

substitution property of equality