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Question

Question 1
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
2 x plus open paren 2 x plus 7 close paren is equal to 135

2x=2x+7
2 x is equal to 2 x plus 7

2x+(2x+7)=180
2 x plus open paren 2 x plus 7 close paren is equal to 180

2x−(2x+7)=135
2 x minus open paren 2 x plus 7 close paren is equal to 135
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
degrees.

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Answer 1

Let's solve the problem step by step.

Question 1

You need to find which equation can be used to determine the value of \( x \).

Given:

• Measure of angle 1 = \( (2x)^\circ \)
• Measure of angle 2 = \( (2x + 7)^\circ \)
• Resulting angle (sum of angle 1 and angle 2) = \( 135^\circ \)

The correct equation to find \( x \) is: \[ 2x + (2x + 7) = 135 \]

So, the response is: 2x + (2x + 7) = 135

Question 2

Now, we solve the equation from Part 1:

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

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

3. Divide by 4: \[ x = 32 \]

Now let's find the measures of each angle:

1. Angle 1: \[ \text{Measure of angle 1} = 2x = 2(32) = 64^\circ \]

2. Angle 2: \[ \text{Measure of angle 2} = 2x + 7 = 2(32) + 7 = 64 + 7 = 71^\circ \]

Final Answers for Part 2:

• \( x = 32 \)
• Angle \( 2x \) has a measure of \( 64 \) degrees.
• Angle \( 2x + 7 \) has a measure of \( 71 \) degrees.

So, the completed answers are:

• \( x = 32 \)
• Angle \( 2x \) = \( 64 \) degrees
• Angle \( 2x + 7 \) = \( 71 \) degrees.