To determine the measure of the two adjacent angles given, we need to identify the correct equation.
When two angles are adjacent and form a linear pair, their measures add up to 180 degrees. Therefore, we will be looking for an equation that represents the sum of the two angles.
Reviewing the options provided:
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(2x + 3) - (x - 6) = 180: This indicates a subtraction and does not correctly represent the relationship between adjacent angles.
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(2x + 3) + (x - 6) = 180: This equation correctly sums the two angles, making it the correct choice for adjacent angles.
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2x + 3 = x - 6: This does not represent the sum of angles and is incorrect for this context.
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(x + 6) - (2x + 3) = 180: This is also a subtraction and incorrect.
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3x - 3 = 180: This does not represent the relationship of the angles either.
Thus, for Part 1, the correct answer is:
(2x + 3) + (x - 6) = 180.
For Part 2, let's solve this equation:
\[ (2x + 3) + (x - 6) = 180 \]
Combine like terms:
\[ 2x + x + 3 - 6 = 180 \]
This simplifies to:
\[ 3x - 3 = 180 \]
Add 3 to both sides:
\[ 3x = 183 \]
Now, divide by 3:
\[ x = 61 \]
Now, we can find the measures of the angles:
- For Angle \(2x + 3\):
\[ 2x + 3 = 2(61) + 3 = 122 + 3 = 125 \text{ degrees} \]
- For Angle \(x - 6\):
\[ x - 6 = 61 - 6 = 55 \text{ degrees} \]
So, the final answers are:
- \(x = 61\)
- Angle \(2x + 3\) is \(125\) degrees.
- Angle \(x - 6\) is \(55\) degrees.
3 answers