Question

The angles shown above form a linear pair. Show all of your work for full credit.

A. What is the angle relationship between these two angles?
B. Set up an equation and solve for n.
C. Substitute your values into the equation and find the measurements of both angles.

Answer 1

A.
`(4n + 22) + (8n - 10) = 180`

B.
`n = 14`

C. 78° and 102°

Explanation:

A. The relationship between the two angles that are a linear pair is: their sum gives us 180°. That is:

`(4n + 22) + (8n - 10) = 180`

B.
`(4n + 22) + (8n - 10) = 180`

Solve for n.

`4n + 22 + 8n - 10 = 180`

Collect like terms

`12n + 12 = 180`

Subtract 12 from both sides

`12n + 12 - 12 = 180 - 12`

`12n = 168`

Divide both sides by 12

`(12n)/(12) = (168)/(12)`

`n = 14`

C. Plug in the value of 14 to get the measurement of both angles

`(4n + 22) = 4(14) + 22 = 56 + 22 = 78`

`(8n - 10) = 8(14) - 10 = 112 - 10 = 102`