Part 1:
To determine the value of \(y\) using angle relationships, we need to analyze the possible equations given. The equations involve angle measures and their relationships. Assuming the angles relate to a straight angle (180 degrees) or a particular format that equals a known value like 120 degrees, we can reason through the options:
- (2x + 10) − (2y + 30) = 120
- 2y + 30 = 120
- (2y + 30) + (2x + 10) = 120
- 2y + 30 = 60
The most straightforward equation to determine y directly would be:
\(2y + 30 = 120\)
This equation isolates \(y\) directly.
Part 2:
Now, we will solve the equation \(2y + 30 = 120\):
-
Subtract 30 from both sides:
\[ 2y = 120 - 30 \]
\[ 2y = 90 \] -
Divide by 2:
\[ y = \frac{90}{2} \]
\[ y = 45 \]
Therefore, the value of \(y\) is 45.
Final Statements:
Angle \(2y + 30\) has a measure of:
\[
2(45) + 30 = 90 + 30 = 120 \text{ degrees.}
\]
So, to complete the statements:
- \(y = 45\)
- Angle \(2y + 30\) has a measure of \(120\) degrees.