Question

two adjacent angles, angle 1, and angle 2 form a resulting angle with a measure of 135
if the measure of angle 1=(2x) and the measure of angle 2 is (2x+7) which equation may be used to determine the value of x
part 1:
a. 2x+(2x+7)=180
b. 2x=2x+7
c. 2x+(2x+7)=135
d. 2x-(2x+7)=135
part 2:
complete the following statements after solving the equation in part 1
x=_
angle 2x has a measure of _ degrees
angle 2x+7 has a measure of _ degrees

Answer 1

To tackle the problem, we first need to understand the relationship between the angles given. We know from the problem description that angle 1 (measured as \(2x\)) and angle 2 (measured as \(2x + 7\)) form a resulting angle of 135°.

Since angle 1 and angle 2 are adjacent angles, they should sum up to the provided measure of 135°. Therefore, we can use this information to set up the equation.

### Part 1:
Given that the measures of angle 1 and angle 2 sum to 135°, the correct equation to use is:
**c. \(2x + (2x + 7) = 135\)**

### Part 2:
Now let's solve the equation \(2x + (2x + 7) = 135\):

1. Combine the terms on the left side:
\[
2x + 2x + 7 = 135
\]
\[
4x + 7 = 135
\]

2. Subtract 7 from both sides:
\[
4x = 135 - 7
\]
\[
4x = 128
\]

3. Divide by 4:
\[
x = \frac{128}{4} = 32
\]

Now we can find the measures of angle 1 and angle 2:

- Measure of angle 1:
\[
2x = 2(32) = 64 \text{ degrees}
\]

- Measure of angle 2:
\[
2x + 7 = 2(32) + 7 = 64 + 7 = 71 \text{ degrees}
\]

### Summary:
Thus, after completing the calculations, we have:
- \(x = 32\)
- Angle \(2x\) has a measure of \(64\) degrees.
- Angle \(2x + 7\) has a measure of \(71\) degrees.