Answer:

To find the value of x in each equation, we'll examine the given equations one by one:

1) mLZ = 56.5"

mLZ does not contain x, so there is no equation to solve for x in this case.

2) FC = 39.2

EP = 7.00x + 25.20

To find x, we need to equate the two expressions for EP and FC:

7.00x + 25.20 = 39.2

Now, let's solve for x:

7.00x = 39.2 - 25.20

7.00x = 14

x = 14 / 7

x = 2

Therefore, in this equation, x = 2.

3) FY = 35.8

FT = 7.00x + 64.60

To find x, we need to equate the two expressions for FY and FT:

7.00x + 64.60 = 35.8

Now, let's solve for x:

7.00x = 35.8 - 64.60

7.00x = -28.8

x = -28.8 / 7

x ≈ -4.11

Therefore, in this equation, x ≈ -4.11.

4) mLPEF = 28.1°

mLPEY = 73.6°

mLPEY = 6.00x + 66.30°

To find x, we need to equate the two expressions for mLPEY:

6.00x + 66.30 = 73.6

Now, let's solve for x:

6.00x = 73.6 - 66.30

6.00x = 7.3

x = 7.3 / 6

x ≈ 1.22

Therefore, in this equation, x ≈ 1.22.

5) mLY = 124.1"

mLm = 6.00x + 43.90"

mLY does not contain x, so there is no equation to solve for x in this case.

6) GD = 30.6

YF = 4.00x + 18.60

To find x, we need to equate the two expressions for GD and YF:

4.00x + 18.60 = 30.6

Now, let's solve for x:

4.00x = 30.6 - 18.60

4.00x = 12

x = 12 / 4

x = 3

Therefore, in this equation, x = 3.

7) KR = 19

KB = 3.00x + 23.00

To find x, we need to equate the two expressions for KR and KB:

3.00x + 23.00 = 19

Now, let's solve for x:

3.00x = 19 - 23.00

3.00x = -4

x = -4 / 3

x ≈ -1.33

Therefore, in this equation, x ≈ -1.33.

8) mLAYL = 35.8°

mLNY = 114.6°

mLNY = 7.00x + 1.60°

To find x, we need to equate the two expressions for mLNY:

7.00x + 1.60 = 114.6

Now, let's solve for x:

7.00x