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Gelneren [198K]
2 years ago
7

NEED HELP! (Question is on attached image and I WILL mark brainliest.)

Mathematics
1 answer:
asambeis [7]2 years ago
7 0

Answer:

• let's consider m‹FBD

{ \tt{m \angle FBD  = 180 \degree -   m \angle ABF}}

• Then let's consider m‹GFE

{ \tt{m \angle GFE  =  180 \degree - m \angle HGF}}

but AD||HE, therefore:

{ \tt{m \angle FBD + m \angle GFE = (180 \degree - m \angle ABF) + (180 \degree - m \angle HGF)}}

but m‹ABF ≈ m‹HGF

{ \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}}}}

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