Question

Part 1: Using the angle relationships, which equation could be used to determine the value of y?

(1 point)
Responses

(2x+10) − (2y+30)=120

2y+30 = 120

(2y+30)+(2x+10) = 120

2y+30 = 60

Question 2
(2 points)
Part 2: Solve the equation from Part 1 and complete the statements below:

y =

Angle 2y + 30 has a measure of
degrees.

Answer 1

### 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:

1. **(2x + 10) − (2y + 30) = 120**
2. **2y + 30 = 120**
3. **(2y + 30) + (2x + 10) = 120**
4. **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 \(2y + 30 = 120\):

1. Subtract 30 from both sides:
\[ 2y = 120 - 30 \]
\[ 2y = 90 \]

2. 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.