Question

124°
(4x + 8)°
relationship: _____________
equation: _________________
x = _____________
2x - 6 x + 1
relationship: _____________
equation: _________________
x = _____________

Explanation:

Left Diagram

Step1: Identify vertical angles

Vertical angles are equal.

Step2: Set up equality equation

$4x + 8 = 124$

Step3: Solve for x

Subtract 8 from both sides:
$4x = 124 - 8$
$4x = 116$
Divide by 4:
$x = \frac{116}{4}$

Step1: Identify supplementary angles

They form a linear pair (supplementary).

Step2: Set up sum to 180

$(2x - 6) + (x + 1) = 180$

Step3: Simplify and solve for x

Combine like terms:
$3x - 5 = 180$
Add 5 to both sides:
$3x = 185$
Divide by 3:
$x = \frac{185}{3}$

Answer:

Relationship: Vertical Angles
Equation: $4x + 8 = 124$
$x = 29$

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Right Diagram