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

Question

(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.