Question

1. congruent or supplementary? equation: __________ 8. congruent or supplementary? equation: __________

Explanation:

Step1: Identify angle - relationship for question 7

Assume the angles are corresponding or vertical angles (congruent). Set up the equation.
$4x + 70=2x - 10$

Step2: Solve the equation for question 7

Subtract $2x$ from both sides.
$4x-2x + 70=2x-2x - 10$
$2x+70=- 10$
Then subtract 70 from both sides.
$2x+70 - 70=-10 - 70$
$2x=-80$
Divide both sides by 2.
$x = - 40$
The angles are congruent.

Step3: Identify angle - relationship for question 8

Assume the angles are same - side interior angles (supplementary). Set up the equation.
$y+(3y + 76)=180$

Step4: Solve the equation for question 8

Combine like - terms.
$y+3y+76 = 180$
$4y+76 = 180$
Subtract 76 from both sides.
$4y+76 - 76=180 - 76$
$4y = 104$
Divide both sides by 4.
$y = 26$
The angles are supplementary.

Answer:

1. Congruent; Equation: $4x + 70=2x - 10$
2. Supplementary; Equation: $y+(3y + 76)=180$