what is the simplified equation corresponding to the measures of the angles?

( 3x - 22) = 90
( 3x - 22) = 180
( 7x - 22) = 90
( 7x - 22) = 180

1 answer

To simplify the equations corresponding to the measures of the angles, we will solve each equation step by step:

  1. For the equation \( 3x - 22 = 90 \): \[ 3x - 22 = 90 \] Adding 22 to both sides: \[ 3x = 112 \] Dividing by 3: \[ x = \frac{112}{3} \approx 37.33 \]

  2. For the equation \( 3x - 22 = 180 \): \[ 3x - 22 = 180 \] Adding 22 to both sides: \[ 3x = 202 \] Dividing by 3: \[ x = \frac{202}{3} \approx 67.33 \]

  3. For the equation \( 7x - 22 = 90 \): \[ 7x - 22 = 90 \] Adding 22 to both sides: \[ 7x = 112 \] Dividing by 7: \[ x = \frac{112}{7} = 16 \]

  4. 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.