Question

Part 1: Which two equations can be used to determine the measure of these two adjacent angles?

(2 points)
Responses

(2x+3)+(x−6)=180

2x+3=x−6

(2x+3)−(x−6)=180

(x+6)−(2x+3)=180

3x−3=180
3 x minus 3 is equal to 180
Question 2
Part 2: Solve one of equations and determine the measure of each angle.(3 points)
x =

Angle 2x + 3 is
degrees.

Angle x - 6 is
degrees.

Answer 1

Part 1: The two equations that can be used to determine the measure of these two adjacent angles, which add up to 180 degrees, are:

1. **(2x + 3) + (x - 6) = 180** (This correctly represents the sum of the two angles.)
2. **(2x + 3) - (x - 6) = 180** (This does not correctly represent the angles but can be manipulated correctly.)

So, the correct choice for determining the adjacent angles is:

**(2x + 3) + (x - 6) = 180.**

Part 2: Let's solve the first equation:

**(2x + 3) + (x - 6) = 180**

Combine like terms:

**2x + 3 + x - 6 = 180**
**3x - 3 = 180**

Now add 3 to both sides:

**3x = 180 + 3**
**3x = 183**

Now divide by 3:

**x = 61.**

Now that we have the value of x, we can find the measures of the angles:

1. Angle \( 2x + 3 \):
- \( 2(61) + 3 = 122 + 3 = 125 \) degrees.

2. Angle \( x - 6 \):
- \( 61 - 6 = 55 \) degrees.

Final answers:

- **x = 61**
- Angle \( 2x + 3 \) is **125 degrees.**
- Angle \( x - 6 \) is **55 degrees.**