Question

°Two adjacent angles, angle 1 and angle 2, form a resulting angle with a measure of 135°
.Part 1: 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?

(1 point)
Responses

2x−(2x+7)=135

2x+(2x+7)=180

2x=2x+7

Question 2
(3 points)
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

Answer 1

### Part 1:

To find the equation that may be used to determine the value of \( x \):

Given that angle 1 measures \( (2x)^\circ \) and angle 2 measures \( (2x + 7)^\circ \), and they form a resulting angle that measures \( 135^\circ \).

Since angle 1 and angle 2 are adjacent angles, you would add them together to find their total measure. The correct equation to use is:

\[
2x + (2x + 7) = 135
\]

### Part 2:

Now, we can solve the equation:

1. Combine like terms:
\[
2x + 2x + 7 = 135
\]
\[
4x + 7 = 135
\]

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

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

Now, let's find the measures of angle 1 and angle 2:

- Angle 1, which is \( 2x \):
\[
2x = 2(32) = 64 \text{ degrees}
\]

- Angle 2, which is \( 2x + 7 \):
\[
2x + 7 = 64 + 7 = 71 \text{ degrees}
\]

### Final Answers:

**x =** 32

**Angle 2x has a measure of** 64 **degrees.**

**Angle 2x + 7 has a measure of** 71 **degrees.**