Question

What are two angles expressed as 3x and (2x - 5)

Answer 1

To express two angles as \(3x\) and \(2x - 5\), you can find their relationship depending on their context. Typically, this could involve setting them equal to each other, or finding other relationships if they are supplementary or complementary angles.

1. **If the angles are equal:** You would set up the equation:
\[
3x = 2x - 5
\]
Solving this:
\[
3x - 2x = -5 \\
x = -5
\]
However, this would produce negative angles, which are not valid in this context.

2. **If the angles are supplementary (adding up to 180 degrees):**
\[
3x + (2x - 5) = 180
\]
Simplifying the left side:
\[
5x - 5 = 180 \\
5x = 185 \\
x = 37
\]
Now substitute \(x\) back to find the angles:
- First angle: \(3x = 3(37) = 111\) degrees
- Second angle: \(2x - 5 = 2(37) - 5 = 74 - 5 = 69\) degrees.

3. **If the angles are complementary (adding up to 90 degrees):**
\[
3x + (2x - 5) = 90
\]
Simplifying:
\[
5x - 5 = 90 \\
5x = 95 \\
x = 19
\]
Now substituting \(x\) back to find the angles:
- First angle: \(3x = 3(19) = 57\) degrees
- Second angle: \(2x - 5 = 2(19) - 5 = 38 - 5 = 33\) degrees.

You can use either relationship depending on the scenario involving these angles. If they are supplementary, the angles would be \(111\) degrees and \(69\) degrees; if they are complementary, the angles would be \(57\) degrees and \(33\) degrees.