To determine the correct equation and solve for \( y \), let's analyze the information given in the problem. Since line \( m \) intersects line \( n \), we typically have relationships involving angles like vertical angles, complementary angles, or supplementary angles.
From the options provided and since it sounds like one angle is given as 85 degrees, the possible relationships could involve either \( 5y + 10 \) being supplementary or complementary to 85 degrees.
Part 1: Identifying the equation
If \( 5y + 10 \) represents an angle adjacent to the 85-degree angle, those two angles would be supplementary (adding up to 180 degrees). Thus, the correct equation would be: \[ (5y + 10) + 85 = 180 \] This means the angle \( 5y + 10 \) plus the 85-degree angle equals 180 degrees.
Part 2: Solve for \( y \)
Now let's solve the equation:
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Start with the equation: \[ (5y + 10) + 85 = 180 \]
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Combine like terms: \[ 5y + 95 = 180 \]
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Subtract 95 from both sides: \[ 5y = 180 - 95 \] \[ 5y = 85 \]
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Divide both sides by 5: \[ y = \frac{85}{5} = 17 \]
Now, substitute \( y \) back into \( 5y + 10 \) to find the angle measure:
- Substitute \( y = 17 \): \[ 5(17) + 10 = 85 + 10 = 95 \]
Final answers:
- \( y = 17 \)
- \( 5y + 10 = 95 \) degrees
So to summarize:
- Equation used: \((5y + 10) + 85 = 180\)
- Value of \( y \): 17
- Measure of the angle \( 5y + 10 \): 95 degrees.
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