Final answer:
The measure of ∠DBF is represented by the expression (188 – 14x)°, obtained by subtracting the sum of ∠ABD and ∠FBE from 180°.
Step-by-step explanation:
To determine the measure of ∠DBF, we need to remember that the sum of angles in a triangle equals 180 degrees. Given the measures of ∠ABD as (6x + 1)° and ∠FBE as (8x – 9)°, we can express the measure of ∠DBF as 180° – ((6x + 1)° + (8x – 9)°). First, we combine the like terms: 6x and 8x to get 14x, and then we combine the constants: 1 and – 9 to get – 8.
The expression becomes 180° – (14x – 8)°. Distributing the negative sign through the parentheses gives us 180° – 14x + 8°, which simplifies to (188 – 14x)°. Thus, the measure of ∠DBF is (188 – 14x)°.