Let's solve the equation step by step to determine the value of \( y \).
Starting with the first equation you provided:
\[ (2y + 30) + (2x + 10) = 120 \]
We can simplify this to:
\[ 2y + 30 + 2x + 10 = 120 \] This simplifies to: \[ 2y + 2x + 40 = 120 \]
Subtract 40 from both sides:
\[ 2y + 2x = 80 \]
At this point, you mention:
\[ 2y + 30 = 60 \]
From this, we can solve for \( y \):
\[ 2y = 60 - 30 \]
\[ 2y = 30 \]
Now, divide both sides by 2:
\[ y = 15 \]
So, the value of \( y \) is:
\[ y = 15 \]
Next, if Angle \( 2y + 30 \) has a measure, we can substitute \( y \) back into the expression \( 2y + 30 \):
\[ 2(15) + 30 = 30 + 30 = 60 \]
Therefore, the final answer is:
- \( y = 15 \)
- Angle \( 2y + 30 \) has a measure of \( 60 \) degrees.