Question
Question What are the two angle measures of complementary angles expressed as 3x° and (2x−5)° ?
Answers
GPT-4o mini
Two angles are complementary if the sum of their measures equals 90 degrees. In this case, the angles are expressed as \(3x\)° and \((2x - 5)\)°.
To find the complementary angles, we set up the equation:
\[
3x + (2x - 5) = 90
\]
Now, combine like terms:
\[
3x + 2x - 5 = 90
\]
\[
5x - 5 = 90
\]
Next, add 5 to both sides:
\[
5x = 95
\]
Now, divide both sides by 5:
\[
x = 19
\]
Now that we have the value of \(x\), we can find the measures of the angles.
For the first angle, \(3x\):
\[
3x = 3(19) = 57°
\]
For the second angle, \((2x - 5)\):
\[
2x - 5 = 2(19) - 5 = 38 - 5 = 33°
\]
The measures of the two complementary angles are \(57°\) and \(33°\).
To find the complementary angles, we set up the equation:
\[
3x + (2x - 5) = 90
\]
Now, combine like terms:
\[
3x + 2x - 5 = 90
\]
\[
5x - 5 = 90
\]
Next, add 5 to both sides:
\[
5x = 95
\]
Now, divide both sides by 5:
\[
x = 19
\]
Now that we have the value of \(x\), we can find the measures of the angles.
For the first angle, \(3x\):
\[
3x = 3(19) = 57°
\]
For the second angle, \((2x - 5)\):
\[
2x - 5 = 2(19) - 5 = 38 - 5 = 33°
\]
The measures of the two complementary angles are \(57°\) and \(33°\).