If \( m \angle F B A=7 x+6 y \), what is \( m \angle F B A \) ? 60 40 44 47

To find \( m \angle F B A \), we need to determine the values of \( x \) and \( y \) that would allow us to calculate \( 7x + 6y \). However, the problem does not provide any additional information or equations involving \( x \) and \( y \). Since we have the options 60, 40, 44, and 47, we can check which of these values can be expressed in the form \( 7x + 6y \) for non-negative integers \( x \) and \( y \). Let's evaluate each option: 1. **For \( m \angle F B A = 60 \)**: \[ 7x + 6y = 60 \] Testing \( x = 0 \) to \( 8 \): - \( x = 0 \): \( 6y = 60 \) → \( y = 10 \) (valid) - \( x = 1 \): \( 7 + 6y = 60 \) → \( 6y = 53 \) (not valid) - \( x = 2 \): \( 14 + 6y = 60 \) → \( 6y = 46 \) (not valid) - \( x = 3 \): \( 21 + 6y = 60 \) → \( 6y = 39 \) (not valid) - \( x = 4 \): \( 28 + 6y = 60 \) → \( 6y = 32 \) (not valid) - \( x = 5 \): \( 35 + 6y = 60 \) → \( 6y = 25 \) (not valid) - \( x = 6 \): \( 42 + 6y = 60 \) → \( 6y = 18 \) → \( y = 3 \) (valid) - \( x = 7 \): \( 49 + 6y = 60 \) → \( 6y = 11 \) (not valid) - \( x = 8 \): \( 56 + 6y = 60 \) → \( 6y = 4 \) (not valid) So, \( m \angle F B A = 60 \) is possible. 2. **For \( m \angle F B A = 40 \)**: \[ 7x + 6y = 40 \] Testing \( x = 0 \) to \( 5 \): - \( x = 0 \): \( 6y = 40 \) → \( y = \frac{40}{6} \) (not valid) - \( x = 1 \): \( 7 + 6y = 40 \) → \( 6y = 33 \) (not valid) - \( x = 2 \): \( 14 + 6y = 40 \) → \( 6y = 26 \) (not valid) - \( x = 3 \): \( 21 + 6y = 40 \) → \( 6y = 19 \) (not valid) - \( x = 4 \): \( 28 + 6y = 40 \) → \( 6y = 12 \) → \( y = 2 \) (valid) - \( x = 5 \): \( 35 + 6y = 40 \) → \( 6y = 5 \) (not valid) So, \( m \angle F B A = 40 \) is possible. 3. **For \( m \angle F B A = 44 \)**: \[ 7x + 6y = 44 \] Testing \( x = 0 \) to \( 6 \): - \( x = 0 \): \( 6y = 44 \) → \( y = \frac{44}{6} \) (not valid) - \( x = 1 \): \( 7 + 6y = 44 \) → \( 6y = 37 \) (not valid) - \( x = 2 \): \( 14 + 6y = 44 \) → \( 6y = 30 \) → \( y = 5 \) (valid) - \( x = 3 \): \( 21 + 6y = 44 \) → \( 6y = 23 \) (not valid) - \( x = 4 \): \(