Question

Need help with 7. and 8. Pleaseeee. Show your work.

Answer 1

Complementary angles are angles that add up to 90°

Supplementary angles are angles that add up to 180°

7.

So with our info, we can form the equation
`3x-4+5x+6=90` to solve for x.

Firstly, combine like terms:
`8x+2=90`

Next, subtract both sides by 2:
`8x=88`

Lastly, divide both sides by 8 and x is going to be
`x=11`

Now that we have the value of x, plug that into both angles to solve for their degrees:

`3*11-4\\ 33-4\\ 29\text{\textdegree}\\ \\ 5*11+6\\ 55+6\\ 61\text{\textdegree}`

In short, ∠DEF is 29° and ∠FEG is 61°.

8.

With our info, we can form the equation as
`9x+1+8x+9=180` to solve for x.

Firstly, combine like terms:
`17x+10=180`

Next, subtract 10 from both sides of the equation:
`17x=170`

Lastly, divide both sides by 17, and the x value is going to be
`x=10`

Now replace the x value with 10 to solve for the angles:

`9*10+1\\ 90+1\\ 91 \text{\textdegree}\\ \\ 8*10+9\\ 80+9\\ 89\text{\textdegree}`

In short, ∠DEF is 91° and ∠FEG is 89°