Steps:
So firstly, let's solve for x. Remember that supplementary angles are angles that have a sum of 180° With this in mind, we can form the equation:
[tex]3x+27+8x-34=180[/tex]
From here, we can solve for x. Firstly, combine like terms:
[tex]11x-7=180[/tex]
Next, add 7 onto both sides of the equation:
[tex]11x=187[/tex]
Lastly, divide both sides by 11:
[tex]x=17[/tex]
Now that we have the value of x, plug it into both of the angles to solve for the angle values:
[tex]A_1=3(17)+27\\A_1=51+27\\A_1=78\textdegree \\\\A_2=8(17)-34\\A_2=136-34\\A_2=102\textdegree \\\\\textsf{Check Work}\\A_1+A_2=180\\78+102=180\\180=180\ \checkmark[/tex]
Answer:
In short:
- x = 17
- Angle 1 = 78°
- Angle 2 = 102°
