Question

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

(1 point)
Responses

2y+30 = 60
2y+30 = 60

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

2y+30 = 120
2y+30 = 120

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

To determine which equation could be used to find the value of \( y \), we need to assess the provided responses with respect to angle relationships. It seems these equations involve terms that suggest they relate to angle measures in a geometric context, but without specific information about the angles themselves (like whether they are supplementary, complementary, etc.), we can only evaluate based on standard practices.

However, based on the equations provided, the equation \( 2y + 30 = 60 \) suggests that the measure of the angle is directly equal to 60 degrees minus some constant, which is straightforward. On the other hand, \( (2y + 30) + (2x + 10) = 120 \) suggests two angle measures summing to another consistent measure.

For clarity, I will choose the equation \( 2y + 30 = 60 \) since it is simpler and seems to match more typical angle relationships.

### Part 2: Solve the equation from Part 1

Using the chosen equation:

\[ 2y + 30 = 60 \]
Subtract 30 from both sides:
\[ 2y = 60 - 30 \]
\[ 2y = 30 \]
Now, divide by 2:
\[ y = 15 \]

So, \( y = 15 \).

### Statement Completion

Now to find the measure of the angle \( 2y + 30 \):

Substituting \( y \) back into the expression:
\[ 2(15) + 30 = 30 + 30 = 60 \]

Thus, the angle \( 2y + 30 \) has a measure of **60 degrees**.

### Final Answers

1. \( y = 15 \)
2. Angle \( 2y + 30 \) has a measure of **60 degrees**.