Question

completing proofs involving linear pairs
given: ( mangle elg = 124^{circ} )
prove: ( x = 28 )
complete the steps in the two - column proof.

Explanation:

Step1: Determine the reason for statement 4

Since \(\angle ELG\) and \(\angle ELD\) are a linear pair (statement 3), 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 \(m\angle ELD + m\angle ELG=180\). So the reason for statement 4 is "linear - pair postulate".

Step2: Determine the statement for step 6

Starting with the equation \(2x + 124=180\) (statement 5).
Using the subtraction property of equality (\(a=b\) implies \(a - c=b - c\)), we subtract 124 from both sides of the equation:
\(2x+124 - 124=180 - 124\).
Simplifying the left - hand side gives \(2x\) and the right - hand side gives \(56\), so the statement for step 6 is \(2x = 56\).

Answer:

1. linear - pair postulate; 6. \(2x = 56\)