To find the measures of the two angles that make up the straight line, we can set up the equation based on the fact that the sum of the two adjacent angles is 180°.
Let the first angle be \( (2x + 3)^\circ \) and the second angle be \( (x - 6)^\circ \).
We set up the equation:
\[ (2x + 3) + (x - 6) = 180 \]
Now, simplify the equation:
\[ 2x + 3 + x - 6 = 180 \]
Combine like terms:
\[ 3x - 3 = 180 \]
Now, add 3 to both sides:
\[ 3x = 183 \]
Next, divide both sides by 3:
\[ x = 61 \]
Now we can find the measures of the two angles by substituting \( x \) back into the expressions for the angles.
For the first angle:
\[ 2x + 3 = 2(61) + 3 = 122 + 3 = 125^\circ \]
For the second angle:
\[ x - 6 = 61 - 6 = 55^\circ \]
So the measures of the two angles that make up the straight line are \( 125^\circ \) and \( 55^\circ \).
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