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

Question

and (2x−5)°
?(1 point)
Responses

33°
and 57°
33 degrees and 57 degrees

19°
and 71°
19 degrees and 71 degrees

30°
and 60°
30 degrees and 60 degrees

21°
and 69°
21 degrees and 69 degrees

Answer 1

Complementary angles are two angles that add up to 90 degrees. Given the angles as \(3x°\) and \((2x - 5)°\), we can set up the following equation:

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

Combine like terms:

\[ 5x - 5 = 90 \]

Add 5 to both sides:

\[ 5x = 95 \]

Now, divide by 5:

\[ x = 19 \]

Now we can find the measures of the two angles:

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

So the two angles are \(57°\) and \(33°\).

Thus, the answer is:

33° and 57°.