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
70°
and 25°
70 degrees and 25 degrees
30°
and 60°
30 degrees and 60 degrees
75°
and 105°
75 degrees and 105 degrees
60°
and 90°
and (x+30)°
. What are the two angle measures?(1 point)
Responses
70°
and 25°
70 degrees and 25 degrees
30°
and 60°
30 degrees and 60 degrees
75°
and 105°
75 degrees and 105 degrees
60°
and 90°
Answers
GPT-4o mini
To find the measures of the two angles that form a right angle, we can use the following equation:
\[
x + (x + 30) = 90
\]
This simplifies to:
\[
2x + 30 = 90
\]
Subtract 30 from both sides:
\[
2x = 60
\]
Now, divide by 2:
\[
x = 30
\]
Now that we have the value of \(x\), we can find the measures of the two angles:
1. The first angle is \(x = 30°\).
2. The second angle is \(x+30 = 30 + 30 = 60°\).
Therefore, the two angle measures are:
**30° and 60°**
\[
x + (x + 30) = 90
\]
This simplifies to:
\[
2x + 30 = 90
\]
Subtract 30 from both sides:
\[
2x = 60
\]
Now, divide by 2:
\[
x = 30
\]
Now that we have the value of \(x\), we can find the measures of the two angles:
1. The first angle is \(x = 30°\).
2. The second angle is \(x+30 = 30 + 30 = 60°\).
Therefore, the two angle measures are:
**30° and 60°**