Question

Solve Equations with Complementary Angles Quick Check
4 of 54 of 5 Items






Question
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°
33 degrees and 57 degrees

Answer 1

Complementary angles add up to 90 degrees.

Given the angles are expressed as \(3x°\) and \((2x - 5)°\), we can set up the equation:

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

Now, combine like terms:

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

Add 5 to both sides:

\[
5x = 95
\]

Now, divide by 5:

\[
x = 19
\]

Now substitute back to find the angle measures:

1. For \(3x\):
\[
3(19) = 57°
\]

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

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

The closest response is:
**33° and 57°.**