Part 1:
To find the equation that may be used to determine the value of \( x \):
Given that angle 1 measures \( (2x)^\circ \) and angle 2 measures \( (2x + 7)^\circ \), and they form a resulting angle that measures \( 135^\circ \).
Since angle 1 and angle 2 are adjacent angles, you would add them together to find their total measure. The correct equation to use is:
\[ 2x + (2x + 7) = 135 \]
Part 2:
Now, we can solve the equation:
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Combine like terms: \[ 2x + 2x + 7 = 135 \] \[ 4x + 7 = 135 \]
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Subtract 7 from both sides: \[ 4x = 135 - 7 \] \[ 4x = 128 \]
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Divide by 4: \[ x = \frac{128}{4} = 32 \]
Now, let's find the measures of angle 1 and angle 2:
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Angle 1, which is \( 2x \): \[ 2x = 2(32) = 64 \text{ degrees} \]
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Angle 2, which is \( 2x + 7 \): \[ 2x + 7 = 64 + 7 = 71 \text{ degrees} \]
Final Answers:
x = 32
Angle 2x has a measure of 64 degrees.
Angle 2x + 7 has a measure of 71 degrees.