Question

given ( mangle elg = 124^{circ} ) prove ( x = 28 ) complete the steps in the two - column proof

Explanation:

Step1: Recall the angle addition postulate

The angle addition postulate states that if two angles form a linear pair, then the sum of their measures is \(180^{\circ}\). Since \(\angle ELG\) and \(\angle ELD\) are a linear pair (statement 3), by the angle addition postulate, \(m\angle ELD + m\angle ELG=180\) (statement 4).

Step2: Solve for \(2x\)

We have the equation \(2x + 124=180\) (statement 5). Using the subtraction property of equality (statement 6), we subtract 124 from both sides of the equation: \(2x+124 - 124=180 - 124\). So, \(2x = 56\).

Answer:

1. angle addition postulate; 6. \(2x = 56\)