Completing Proofs Involving Linear PairsGiven: m ZELG = 124°

Prove: x = 28

Statements

Reasons

1. m ZELG = 124

1. given

2. m ZELD = 2x

2. given

H

L

3. ZELG and ZELD are

a linear pair

3. definition of a linear pair

(2x)

G

4. m ZELD + m ZELG = 180

4.

Ε

• F.

5. 2x + 124 = 180

5. substitution

Complete the steps in the two-column proof.

6.

6. subtraction property

7. x = 28

7. division property

Intro

Done

vity

The corresponding angles of the lines solved and the value of x = 28°

What are angles in parallel lines?

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the measure of ∠ELG = 124°

The measure of ∠ELD = 2x

∠ELG and ∠ELD are a linear pairs of angles

So , the measure of ∠ELG  + ∠ELD = 180°

On simplifying , we get

2x + 124° = 180°

Subtracting 124° on both sides , we get

2x = 56°

Divide by 2 on both sides , we get

x = 28°

Therefore , the value of x is 28°

Hence , the angle is x = 28°

To learn more about angles in parallel lines click :

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Answer:

1. angle addition post

2. 2x=56