To determine the measures of the two angles that form a straight line (180°), we start by setting up an equation based on the information given. The angles are (2x + 3)° and (x - 6)°.
Since both angles form a straight line, their sum should equal 180°:
\[ (2x + 3) + (x - 6) = 180 \]
Now, we'll combine like terms:
\[ 2x + x + 3 - 6 = 180 \] \[ 3x - 3 = 180 \]
Next, we add 3 to both sides:
\[ 3x = 183 \]
Now, we divide by 3:
\[ x = 61 \]
Now we will substitute \( x = 61 \) back into the expressions for the angles to find their measures:
- First angle:
\[ 2x + 3 = 2(61) + 3 = 122 + 3 = 125° \]
- Second angle:
\[ x - 6 = 61 - 6 = 55° \]
Thus, the measures of the two angles that make up the straight line are:
- 125°
- 55°
The correct response is:
125° and 55°
1 answer