Answer:
• let's consider m‹FBD
[tex]{ \tt{m \angle FBD = 180 \degree - m \angle ABF}}[/tex]
• Then let's consider m‹GFE
[tex]{ \tt{m \angle GFE = 180 \degree - m \angle HGF}}[/tex]
but AD||HE, therefore:
[tex]{ \tt{m \angle FBD + m \angle GFE = (180 \degree - m \angle ABF) + (180 \degree - m \angle HGF)}}[/tex]
but m‹ABF ≈ m‹HGF
[tex]{ \tt{2(m \angle FBD) +2( m \angle GFE) = 180 \degree + 180 \degree}} \\ \\ { \tt{2(m \angle FBD + m \angle GFE) = 360 \degree}} \\ \\ { \tt{m \angle FBD + m \angle GFE = \frac{360 \degree}{2} }} \\ \\ { \boxed{ \boxed{ \bf{m \angle FBD + m \angle GFE = 180 \degree}}}}[/tex]
