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

Question

.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.