Question

How do you solve this?

Answer 1

`x = 18`

`y = 7.5`

`z = 7`

Explanation:

✍️
`(8x - 7) + (3x - 11) = 180` (consecutive interior angles are supplementary)

Solve for x

`8x - 7 + 3x - 11 = 180`

Add like terms

`11x - 18 = 180`

Add 18 to both sides

`11x = 180 + 18`

`11x = 198`

Divide both sides by 11

✅
`x = 18`

✍️
`(2y + 23) = (4y + 8)` (alternate interior angles are congruent)

Solve for y

`2y + 23 = 4y + 8`

Collect like terms

`23 - 8 = 4y - 2y`

`15 = 2y`

Divide both sides by 2

✅y = 7.5

✍️
`(2y + 23) + (3z^2 - 5) = 180` (linear pair angles)

Plug in the value of y

`(2(7.5) + 23) + (3z^2 - 5) = 180`

`(15 + 23) + (3z^2 - 5) = 180`

`38 + 3z^2 - 5 = 180`

Add like terms

`3z^2 + 33 = 180`

Subtract 33 from each side

`3z^2 = 180 - 33`

`3z^2 = 147`

Divide both sides by 3

`z^2 = (147)/(3)`

`z^2 = 49`

Square both sides

`√(z^2) = √(49)`

`z = 7`