The two measures form a sum of 180°, which means that they are supplementary angles. To find the measures, set up the equation below:
1.) Solve for x
[tex]5x + (3x + 12) = 180[/tex]
Then use the [tex]PEMDAS[/tex] method for order of operations.
Since [tex](3x + 12)[/tex] is already in simplest form, we can take away the parenthesis.
Then we will have:
[tex]5x + 3x + 12 = 180[/tex]
Notice how the coefficients 5x and 3x both have the same variable. This means that we can add them up.
[tex]8x + 12 = 180[/tex]
If 12 more than 8x is 180, then this means twelve less than 180 is equal to 8x. Subtract 12 fro both sides:
[tex]8x + 12 - 12 = 180 - 12[/tex]
[tex]8x = 168[/tex]
168 is the product of 8 and x, so divide both sides by 8.
[tex]\frac{8}{8}x = \frac{168}{8}[/tex]
x = 21 degrees
2.) Plug in the value of x.
5(21) + (3(21) + 12)
First do the operations inside the parenthesis:
[tex]5(21) + (63 + 12)[/tex]
= [tex]5(21) + 75[/tex]
= [tex]105 + 75[/tex] = 180
The two angle measures are [tex]105[/tex]° and [tex]75[/tex]°. Hope this helped.
