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 [tex] 3x-4+5x+6=90 [/tex] to solve for x.
Firstly, combine like terms: [tex] 8x+2=90 [/tex]
Next, subtract both sides by 2: [tex] 8x=88 [/tex]
Lastly, divide both sides by 8 and x is going to be [tex] x=11 [/tex]
Now that we have the value of x, plug that into both angles to solve for their degrees:
[tex] 3*11-4\\ 33-4\\ 29\text{\textdegree}\\ \\ 5*11+6\\ 55+6\\ 61\text{\textdegree} [/tex]
In short, ∠DEF is 29° and ∠FEG is 61°.
8.
With our info, we can form the equation as [tex] 9x+1+8x+9=180 [/tex] to solve for x.
Firstly, combine like terms: [tex] 17x+10=180 [/tex]
Next, subtract 10 from both sides of the equation: [tex] 17x=170 [/tex]
Lastly, divide both sides by 17, and the x value is going to be [tex] x=10 [/tex]
Now replace the x value with 10 to solve for the angles:
[tex] 9*10+1\\ 90+1\\ 91 \text{\textdegree}\\ \\ 8*10+9\\ 80+9\\ 89\text{\textdegree} [/tex]
In short, ∠DEF is 91° and ∠FEG is 89°
