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1. x = 54, y = 114,

missing angles => 66° and 114°

2. x = 42, y = 14,

Missing angles => 84°, 86°

3. x = 40, y = 50

Missing angles => 105°, 75°

Step-by-step explanation:

1. y° = 114° (corresponding angles are congruent)

(x + 12)° + y° = 180° (linear pair angles)

Substitute

x + 12 + 114 = 180

x + 126 = 180

Subtract 126 from each side

x = 180 - 126

x = 54

✔️Find the missing angles by plugging in the values of x and y in each case

(x + 12)° = 54 + 12 = 66°

y = 114°

2. ✔️Find x:

(2x)° + 96° = 180° (consecutive interior angles are supplementary)

Subtract 96 from each side

2x = 180 - 96

2x = 84

x = 84/2

x = 42

✔️Find y:

(3y + 44)° + 94° = 180° (consecutive interior angles are supplementary)

3y + 44 + 94 = 180

3y + 138 = 180

3y = 180 - 138

3y = 42

y = 42/3

y = 14

✔️Missing angles:

(2x)°

Plug in the value of x

= 2(42) = 84°

(3y + 44)°

Plug in the value of y

3(14) + 44 = 86°

3.

✔️Find x:

3x - 15 = 105 (corresponding angles are congruent)

3x = 105 + 15

3x = 120

x = 120/3

x = 40

✔️Find y:

(3x - 15)° + (y + 25)° = 180° (linear pair angles are supplementary)

Plug in the value of x to solve for y

3(40) - 15 + y + 25 = 180

120 - 15 + y + 25 = 180

Add like terms

130 + y = 180

y = 180 - 130

y = 50

✔️Missing angles:

(3x - 15)°

Plug in the value of x

3(40) - 15 = 105°

(y + 25)°

Plug in the value of y

50 + 25 = 75°

c

step-by-step explanation: