Use the image to answer the question.

Question

a. Write an equation for these two supplementary angles. (1 point)

b. Explain how to solve for the value of x. (1 point)

c. Find the measurement of each angle. Make sure to list both. (2 points)

(4 points)

Answer 1

a. The equation for these two supplementary angles can be written as:

180 - x = x + 60

b. To solve for the value of x, we can set up and solve the equation:

180 - x = x + 60

Combine like terms:
180 = 2x + 60

Subtract 60 from both sides:
120 = 2x

Divide both sides by 2:
60 = x

c. To find the measurement of each angle, we substitute the value of x into the equation:

180 - x = 180 - 60 = 120

x + 60 = 60 + 60 = 120

The measurement of each angle is 120 degrees.

Answer 2

Use the image to answer the question.
the image shows
2x+3 is the angle on the left x-6 is the angle on the left

a. Write an equation for these two supplementary angles. (1 point)

b. Explain how to solve for the value of x. (1 point)

c. Find the measurement of each angle. Make sure to list both. (2 points)

(4 points)

Answer 3

a. The equation for these two supplementary angles can be written as:

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

b. To solve for the value of x, we can simplify and solve the equation:

2x + 3 = 180 - x + 6

Combine like terms:
2x + 3 = 186 - x

Add x to both sides:
3x + 3 = 186

Subtract 3 from both sides:
3x = 183

Divide both sides by 3:
x = 61

c. To find the measurement of each angle, we substitute the value of x into the equations:

2x + 3 = 2(61) + 3 = 122 + 3 = 125 degrees

x - 6 = 61 - 6 = 55 degrees

The measurement of the angle on the left is 125 degrees, and the measurement of the angle on the right is 55 degrees.