Question
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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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Answers
GPT-4o mini
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.
### 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.