To find an equation for the two adjacent angles \( (2x + 3)^\circ \) and \( (x - 6)^\circ \), you can add the two expressions together and set them equal to the sum of adjacent angles. Since adjacent angles typically sum to \( 180^\circ \) if they form a linear pair, we can use this.
So the equation can be written as:
\[ (2x + 3) + (x - 6) = 180 \]
Now we can simplify this equation:
- Combine like terms:
\[ 2x + 3 + x - 6 = 180 \] \[ (2x + x) + (3 - 6) = 180 \] \[ 3x - 3 = 180 \]
- Add \( 3 \) to both sides:
\[ 3x - 3 + 3 = 180 + 3 \] \[ 3x = 183 \]
- Divide by \( 3 \):
\[ x = 61 \]
So the equation for the two adjacent angles can be concluded as:
\[ (2x + 3)^\circ + (x - 6)^\circ = 180^\circ \]
Therefore, the completed equation is:
\[ (2x + 3) + (x - 6) = 180 \]