As shown in the figure, line AC and line FG are parallel to each other and m ∠ABF = 55°. If ray BD and segment EF are parallel and m ∠DBF = 30°, then find m ∠EFG.
Explanation:
Ray BD and EF are parallel lines and line BF is the transversal.
∴ m ∠DBF = m ∠EFB = 30° (∠DBF and ∠EFB form a pair of Alternate angles)
m ∠ABF = m ∠BFG = 55°, as they form a pair of alternate angles across lines AC and FG with BF as the transversal.
Now, m ∠BFG = m ∠BFE + m ∠EFG
∴ m ∠EFG = 55° − 30° = 25°
Hence, option (a).
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