You set up the equation by adding the angle measures(2x+3) and (x-6) and setting equal to 180. You must combine like terms in order to solve the equation for x. Finally, you substitute the value of x back into the original expressions to find the angle measures.
To set up the equation, you add the angle measures (2x+3) and (x-6), which gives you:
(2x+3) + (x-6) = 180
Next, you combine like terms by adding the coefficients of x and the constant terms. This gives you:
3x - 3 = 180
To solve the equation for x, you isolate the variable by adding 3 to both sides of the equation:
3x = 183
Then, you divide both sides by 3 to solve for x:
x = 61
Now that you have found the value of x, you substitute it back into the original expressions to find the angle measures:
Angle measure 1: 2x + 3 = 2(61) + 3 = 123 + 3 = 126
Angle measure 2: x - 6 = 61 - 6 = 55