Question

What is an equation for these two adjacent angles?

(2 points)
(2x+3)° + (x−6)° = ___

Answer 1

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:

1. Combine like terms:

\[
2x + 3 + x - 6 = 180
\]
\[
(2x + x) + (3 - 6) = 180
\]
\[
3x - 3 = 180
\]

2. Add \( 3 \) to both sides:

\[
3x - 3 + 3 = 180 + 3
\]
\[
3x = 183
\]

3. 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:

\[
(2x + 3) + (x - 6) = 180
\]