Question

completing proofs involving linear pairs given: m∠elg = 124° prove: x = 28 statements reasons 1. m∠elg = 124 1. given 2. m∠eld = 2x 2. given 3. ∠elg and ∠eld are a linear pair. 3. definition of a linear pair 4. m∠eld + m∠elg = 180 4. 5. 2x + 124 = 180 5. substitution 6. 6. subtraction property 7. x = 28 7. division property complete the steps in the two - column proof.

Explanation:

Step1: Recall linear - pair property

The sum of angles in a linear pair is 180°. So for linear - pair ∠ELD and ∠ELG, we have $m\angle ELD + m\angle ELG=180$.

Step2: Substitute given values

We know that $m\angle ELD = 2x$ and $m\angle ELG = 124$, so $2x+124 = 180$.

Step3: Apply subtraction property

Subtract 124 from both sides of the equation $2x+124 = 180$. We get $2x=180 - 124$, which simplifies to $2x = 56$.

Step4: Apply division property

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

Answer:

$x = 28$