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6) 130

7) x = 35

8) y = 100

9) 50

10) 130

11) DEF = 29

12) FEG = 61

13) DEF = 91

14) FEG = 89

Step-by-step explanation:

angle AEB is 50°

supplementary is when 2 angles add together to make 180°

50 + x = 180

x = 180 - 50

x = 130

angles AEB and DEC are vertical angles

vertical angles are equal.

50 = x + 15

50 - 15 = x

35 = x

AEB and AED are supplementary angles

supplementary angles add together to make 180

50 + (y + 30) = 180

y + 30 = 180 - 50

y + 30 = 130

y = 130 - 30

y = 100

DEC is vertical to AEB

vertical angles are equal.

AEB = 50

DEC = 50

AED = y + 30

as established earlier, y = 100

substitute Y for 100

AED = 100 + 30

AED = 130

DEF and FEG are complimentary.

complimentary means they add together to make 90

(3x - 4 ) + (5x + 6 ) = 90

3x - 4 + 5x + 6 = 90

8x + 2 = 90

8x = 90 - 2

8x = 88

x = 88/8

x = 11

substitute x into the equations

DEF = 3x - 4

DEF = 33 - 4

DEF = 29

FEG = 5x + 6

FEG = 55 + 6

FEG = 61

DEF and FEG are supplementary.

supplementary means they add together to make 180

(9x + 1) + (8x + 9) = 180

9x + 8x + 1 + 9 = 180

17x + 10 = 180

17x = 170

x = 10

substitute x into the equations

DEF =  9x + 1

DEF = 90 + 1

DEF = 91

FEG = 8x + 9

FEG = 80 + 9

FEG = 89

146%

step-by-step explanation: