Complementary angles are two angles whose measures add up to 90 degrees. In this case, you have the angles expressed as \(3x\) and \(2x - 5\).
To find the values of \(x\), we can set up the equation:
\[ 3x + (2x - 5) = 90 \]
Combining like terms gives:
\[ 5x - 5 = 90 \]
Next, add 5 to both sides:
\[ 5x = 95 \]
Now, divide by 5:
\[ x = 19 \]
Now we can find the measures of the angles:
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First angle: \[ 3x = 3(19) = 57 \]
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Second angle: \[ 2x - 5 = 2(19) - 5 = 38 - 5 = 33 \]
So the two angles are \(57\) degrees and \(33\) degrees.
Among the answer options provided:
- 33 and 57 (Correct)
- 21 and 69 (Incorrect)
- 30 and 60 (Incorrect)
- 19 and 71 (Incorrect)
The correct answer is 33 and 57.