To determine the correct equation to find the value of \( y \), it's important to analyze the relationships established. Since the context of the problem isn't fully provided, I'll help you reason through the common angle relationships that might apply.
Part 1: Choosing the Equation
- The equation 2y + 30 = 60 suggests that angle \( 2y + 30 \) measures 60 degrees.
- The equation (2y + 30) + (2x + 10) = 120 implies that the sum of two angles equals 120 degrees. This could be valid if they are adjacent angles that add up.
- The equation (2x + 10) - (2y + 30) = 120 does not seem consistent with common angle relationships.
- Finally, 2y + 30 = 120 would suggest that the angle \( 2y + 30 \) measures 120 degrees.
Without more information, both \( (1) \) and \( (4) \) could be reasonable options. If \( 2y + 30 \) represents an angle that, for example, is equal to one you know or could relate to other angles, you would select accordingly.
If \( 2y + 30=60 \) is chosen:
- From \( 2y + 30 = 60 \): \[ 2y = 60 - 30 \] \[ 2y = 30 \] \[ y = 15 \]
If \( 2y + 30 = 120 \):
- From \( 2y + 30 = 120 \): \[ 2y = 120 - 30 \] \[ 2y = 90 \] \[ y = 45 \]
Conclusion for Part 2:
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If you use \( 2y + 30 = 60 \) then:
- \( y = 15 \)
- Angle \( 2y + 30 \) has a measure of \( 60 \) degrees.
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If you use \( 2y + 30 = 120 \):
- \( y = 45 \)
- Angle \( 2y + 30 \) has a measure of \( 120 \) degrees.
Please confirm which specific equation to solve based on your angle relationships, or provide more details, and I'd be glad to assist further!