Question

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

Answer 1

Answer:

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

B. $n = 14$

C. 78° and 102°

Step-by-step 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

$\frac{12n}{12} = \frac{168}{12}$

$n = 14$

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

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

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