Question

completing proofs involvi
given: m∠elg = 124°
prove: x = 28
complete the steps in the two - column proof.

Explanation:

Step1: Identify angle - related property

Assume that $\angle ELG$ and $\angle ELD$ are supplementary (linear - pair of angles). Since the sum of angles in a linear pair is $180^{\circ}$, and we know that $\angle ELG = 124^{\circ}$, then $\angle ELD=180^{\circ}-\angle ELG$.
$\angle ELD = 180 - 124=56^{\circ}$

Step2: Set up an equation based on the given angle measure

We are given that $\angle ELD=(2x)^{\circ}$. So, we set up the equation $2x = 56$.

Step3: Solve the equation for x

Divide both sides of the equation $2x = 56$ by 2.
$x=\frac{56}{2}=28$

Answer:

$x = 28$