What are the two angle measures of complementary angles expressed as 3x°

Question

and (2x−5)°
?(1 point)
Responses

30°
and 60°
30 degrees and 60 degrees

19°
and 71°
19 degrees and 71 degrees

21°
and 69°
21 degrees and 69 degrees

33°
and 57°

Answer 1

To find the measures of the complementary angles expressed as \(3x^\circ\) and \((2x - 5)^\circ\), we start with the fact that complementary angles sum up to 90 degrees.

We can set up the equation:

\[ 3x + (2x - 5) = 90 \]

Now, let's simplify and solve for \(x\):

\[ 3x + 2x - 5 = 90 \] \[ 5x - 5 = 90 \] \[ 5x = 90 + 5 \] \[ 5x = 95 \] \[ x = \frac{95}{5} = 19 \]

Now, we substitute \(x\) back into the expressions for the angles:

1. First angle: \[ 3x = 3(19) = 57^\circ \]

2. Second angle: \[ 2x - 5 = 2(19) - 5 = 38 - 5 = 33^\circ \]

Thus, the two angles are \(33^\circ\) and \(57^\circ\).

Among the provided responses, the correct answer is:

33° and 57°.