What are the two angle measures of complementary angles expressed as 3x° and (2x−5)° ?(1 point)

Question

Responses

33° and 57°
33 degrees and 57 degrees

30° and 60°
30 degrees and 60 degrees

19° and 71°
19 degrees and 71 degrees

21° and 69°

Answer 1

Complementary angles are two angles whose measures add up to 90 degrees. We can set up the equation using the given expressions for the angles:

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

Now, let's combine like terms:

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

Next, add 5 to both sides:

\[ 5x = 95 \]

Now, divide by 5:

\[ x = 19 \]

Now we can find the measures of the two angles:

1. First angle: \( 3x = 3(19) = 57° \)
2. Second angle: \( 2x - 5 = 2(19) - 5 = 38 - 5 = 33° \)

Thus, the measures of the complementary angles are 57° and 33°.

The correct response is:

33° and 57°.