To determine the equation that should be used to find the value of \( y \) in the context of two intersecting lines, we need to identify the relationship between the angles involved.
From the choices provided:
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\( 5y + 10 = 85 \): This implies that one angle is \( 5y + 10 \) degrees and is equal to \( 85 \) degrees.
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\( (5y + 10) + 85 = 90 \): This implies that the sum of the angle \( 5y + 10 \) and \( 85 \) degrees equals \( 90 \) degrees, suggesting they are complementary angles.
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\( (5y + 10) - 85 = 180 \): This implies that subtracting \( 85 \) degrees from \( 5y + 10 \) gives \( 180 \) degrees, which does not seem applicable in this context.
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\( (5y + 10) + 85 = 180 \): This suggests that the angle \( 5y + 10 \) and \( 85 \) degrees are supplementary angles that add up to \( 180 \) degrees, which is likely the case for two angles formed by intersecting lines.
Part 1 Answer: The best choice to determine the value of \( y \) is \( (5y + 10) + 85 = 180 \).
Part 2: Now, we will use the chosen equation to solve for \( y \):
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Start with the equation: \[ (5y + 10) + 85 = 180 \]
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Simplify the equation: \[ 5y + 10 + 85 = 180 \] \[ 5y + 95 = 180 \]
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Subtract \( 95 \) from both sides: \[ 5y = 180 - 95 \] \[ 5y = 85 \]
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Divide both sides by \( 5 \): \[ y = \frac{85}{5} \] \[ y = 17 \]
To find the measure of the angle: \[ 5y + 10 = 5(17) + 10 = 85 + 10 = 95 \text{ degrees} \]
Final Answer:
- \( y = 17 \)
- \( 5y + 10 = 95 \) degrees