To simplify the equations corresponding to the measures of the angles, we will solve each equation step by step:
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For the equation \( 3x - 22 = 90 \): \[ 3x - 22 = 90 \] Adding 22 to both sides: \[ 3x = 112 \] Dividing by 3: \[ x = \frac{112}{3} \approx 37.33 \]
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For the equation \( 3x - 22 = 180 \): \[ 3x - 22 = 180 \] Adding 22 to both sides: \[ 3x = 202 \] Dividing by 3: \[ x = \frac{202}{3} \approx 67.33 \]
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For the equation \( 7x - 22 = 90 \): \[ 7x - 22 = 90 \] Adding 22 to both sides: \[ 7x = 112 \] Dividing by 7: \[ x = \frac{112}{7} = 16 \]
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For the equation \( 7x - 22 = 180 \): \[ 7x - 22 = 180 \] Adding 22 to both sides: \[ 7x = 202 \] Dividing by 7: \[ x = \frac{202}{7} \approx 28.86 \]
Summary of Solutions
- For \( 3x - 22 = 90 \): \( x \approx 37.33 \)
- For \( 3x - 22 = 180 \): \( x \approx 67.33 \)
- For \( 7x - 22 = 90 \): \( x = 16 \)
- For \( 7x - 22 = 180 \): \( x \approx 28.86 \)
These calculations represent the simplified equations corresponding to the measures of the angles.