Question

What are the two angle measures of complementary angles expressed as 3x degrees and (2x-5) degrees
33 and 57
30 and 60
19 and 71
21 and 69

Answer 1

Complementary angles are two angles whose measures add up to 90 degrees.

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

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

Simplifying the equation:

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

Now, we can find the measures of the angles:

1. First angle:
\[
3x = 3(19) = 57 \text{ degrees}
\]

2. Second angle:
\[
2x - 5 = 2(19) - 5 = 38 - 5 = 33 \text{ degrees}
\]

So, the two angle measures are \(57\) degrees and \(33\) degrees.

Among the provided options, the correct pair is:

**33 and 57**.