Question
Solve Equations with Adjacent Angles Quick Check
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Question
A right angle is formed by two adjacent angles with measures of (x)°
and (x+30)°
. What are the two angle measures?(1 point)
Responses
60°
and 90°
60 degrees and 90 degrees
30°
and 60°
30 degrees and 60 degrees
70°
and 25°
70 degrees and 25 degrees
75°
and 105°
75 degrees and 105 degrees
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Answers
GPT-4o mini
To solve for the measures of the two adjacent angles that form a right angle, we start with the information provided in the problem.
We have:
- One angle is \( x \) degrees
- The other angle is \( x + 30 \) degrees
- Together, these angles form a right angle, which measures \( 90 \) degrees.
This gives us the equation:
\[
x + (x + 30) = 90
\]
Now, we can simplify and solve for \( x \):
\[
2x + 30 = 90
\]
Subtract \( 30 \) from both sides:
\[
2x = 60
\]
Now divide by \( 2 \):
\[
x = 30
\]
Now that we have \( x \), we can find the measures of both angles:
1. The first angle is \( x = 30^\circ \).
2. The second angle is \( x + 30 = 30 + 30 = 60^\circ \).
Thus, the two angle measures are:
**30° and 60°**
The correct response is:
30° and 60°.
We have:
- One angle is \( x \) degrees
- The other angle is \( x + 30 \) degrees
- Together, these angles form a right angle, which measures \( 90 \) degrees.
This gives us the equation:
\[
x + (x + 30) = 90
\]
Now, we can simplify and solve for \( x \):
\[
2x + 30 = 90
\]
Subtract \( 30 \) from both sides:
\[
2x = 60
\]
Now divide by \( 2 \):
\[
x = 30
\]
Now that we have \( x \), we can find the measures of both angles:
1. The first angle is \( x = 30^\circ \).
2. The second angle is \( x + 30 = 30 + 30 = 60^\circ \).
Thus, the two angle measures are:
**30° and 60°**
The correct response is:
30° and 60°.