Completing Proofs Involving Linear Pairs Given: 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

1: angle addition postulate

2: 2x=56

Step-by-step explanation:

(a) Carl earns $45 per 3 hours as given. To find the amount he earns per hour, we simply divide:

$45/3 hours = $15/hour

(b) To see how much Louis makes per hour, simply plug in 1 for the hours value x:

y = 12(1 hours)

y = $12/hour

Thus Carl makes more than Louis.

(c) The equation of Carl's dollars per hour is similar to Louis':

y = 15x 

where x is the number of hours he works and y is the number of dollars he earns. Plug in whole number values of hours for x and plot the points (x, y) on a graph.