To answer your question, we need to examine the properties of angles formed when two lines intersect. The angles around the point of intersection provide relationships that can help us formulate the right equation.
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Identifying the relationship: If one angle measures \( 85^\circ \) and another angle is expressed as \( 5y + 10 \), we can assume that they are either supplementary (adding up to \( 180^\circ \)) or they might be vertical angles (equal). Based on the equations you provided, it seems likely that \( 5y + 10 \) and \( 85^\circ \) are supplementary.
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Choosing the right equation: The correct equation to use, assuming \( 5y + 10 \) and \( 85^\circ \) are supplementary, would be: \[ (5y + 10) + 85 = 180 \]
So, the response to Part 1 would be:
- (5y + 10) + 85 = 180
For Part 2
Now, we will solve for \( y \) using the equation (5y + 10) + 85 = 180:
\[ 5y + 10 + 85 = 180 \] \[ 5y + 95 = 180 \] \[ 5y = 180 - 95 \] \[ 5y = 85 \] \[ y = \frac{85}{5} = 17 \]
Now, substitute back to find the angle measure: \[ 5y + 10 = 5(17) + 10 = 85 + 10 = 95 \]
Thus, the values are:
- \( y = 17 \)
- \( 5y + 10 = 95 \) degrees
Final Answers:
- Part 1 (Equation): (5y + 10) + 85 = 180
- Part 2: \( y = 17 \), \( 5y + 10 = 95 \) degrees