Question

Angle 1 and 2 are supplementary angles . If angle 1 measures 3x+27and angle 2 measure 8x-34 what is the value of x and what is the measurement of each angle

Answer 1

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:

`3x+27+8x-34=180`

From here, we can solve for x. Firstly, combine like terms:

`11x-7=180`

Next, add 7 onto both sides of the equation:

`11x=187`

Lastly, divide both sides by 11:

`x=17`

Now that we have the value of x, plug it into both of the angles to solve for the angle values:

`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`

Answer:

In short:

• x = 17
• Angle 1 = 78°
• Angle 2 = 102°