19. If \( m \angle 2=8 x-20 \), and \( m \angle 3=5 x+5 \), what is \( m \angle 2 \) ? What is \( m \angle 3 \) ?

To find the measures of angles 2 and 3, we need to set up an equation based on the information given. However, we need to know the relationship between angles 2 and 3. If we assume that angles 2 and 3 are supplementary (which means they add up to 180 degrees), we can set up the equation: \[ m \angle 2 + m \angle 3 = 180 \] Substituting the expressions for \( m \angle 2 \) and \( m \angle 3 \): \[ (8x - 20) + (5x + 5) = 180 \] Now, combine like terms: \[ 8x + 5x - 20 + 5 = 180 \] \[ 13x - 15 = 180 \] Next, add 15 to both sides: \[ 13x = 195 \] Now, divide by 13: \[ x = 15 \] Now that we have the value of \( x \), we can find \( m \angle 2 \) and \( m \angle 3 \). First, calculate \( m \angle 2 \): \[ m \angle 2 = 8x - 20 = 8(15) - 20 = 120 - 20 = 100 \] Next, calculate \( m \angle 3 \): \[ m \angle 3 = 5x + 5 = 5(15) + 5 = 75 + 5 = 80 \] Thus, the measures of the angles are: \[ m \angle 2 = 100^\circ \] \[ m \angle 3 = 80^\circ \]