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

and (2x−5)°
?(1 point)
Responses

19°
and 71°
19 degrees and 71 degrees

21°
and 69°
21 degrees and 69 degrees

30°
and 60°
30 degrees and 60 degrees

33°
and 57°

1 answer

Complementary angles are two angles whose measures add up to 90 degrees. To find the values of the angles expressed as \(3x\) and \((2x - 5)\), we set up the equation:

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

Now, simplify the equation:

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

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

  1. For the first angle: \[ 3x = 3(19) = 57° \]

  2. For the second angle: \[ 2x - 5 = 2(19) - 5 = 38 - 5 = 33° \]

Thus, the two angle measures are \(33°\) and \(57°\).

The correct response is:

33° and 57°