Question

given: ( mangle elg = 124^circ ) prove: ( x = 28 ) complete the steps in the two - column proof. statements 1. ( mangle elg = 124 ) 2. ( mangle eld = 2x ) 3. ( angle elg ) and ( angle eld ) are a linear pair. 4. ( mangle eld + mangle elg = 180 ) 5. ( 2x + 124 = 180 ) 6. ( diamond ) 7. ( x = 28 ) reasons 1. given 2. given 3. definition of a linear pair 4. ( diamond ) 5. substitution 6. subtraction property 7. division property definition of vertical angles definition of congruence linear pair postulate addition property of equality

Explanation:

Step1: Identify the linear - pair relationship

By the definition of a linear pair, if two angles form a linear pair, their measures add up to \(180^{\circ}\). So, \(m\angle ELD+m\angle ELG = 180\) (Reason: definition of a linear pair).

Step2: Substitute the given values

Given \(m\angle ELG=124\) and \(m\angle ELD = 2x\), substitute into the equation \(m\angle ELD+m\angle ELG = 180\). We get \(2x + 124=180\) (Reason: substitution).

Step3: Solve for \(x\) using the subtraction property

Subtract 124 from both sides of the equation \(2x + 124=180\).

$$
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$$

(Reason: subtraction property of equality).

Step4: Solve for \(x\) using the division property

Divide both sides of the equation \(2x = 56\) by 2.

$$
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$$

(Reason: division property of equality).

Answer:

The steps in the two - column proof are completed as follows:

Statements	Reasons
2. \(m\angle ELD=2x\)	2. given
3. \(\angle ELG\) and \(\angle ELD\) are a linear pair	3. definition of a linear pair
4. \(m\angle ELD+m\angle ELG = 180\)	4. linear pair postulate
5. \(2x + 124=180\)	5. substitution
6. \(2x=56\)	6. subtraction property of equality
7. \(x = 28\)	7. division property of equality