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.
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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.
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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.
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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.
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