The measure of ∠FEG (m∠FEG) is 35°. The correct option is the third option m∠FEG = 35°
From the question,
We are to determine the measure of ∠FEG
Consider ΔEFG
In ΔEFG,
∠FEG + ∠EFG + ∠EGF = 180° (Sum of angles in a triangle)
Since, EFGH is a rhombus, that means /EF/ = /FG/
Thus, ΔEFG is an isosceles triangle
Then,
∠FEG = ∠EGF (Base angles of an isosceles triangle)
Then we can write that
∠FEG + ∠EFG + ∠FEG = 180°
2 × ∠FEG + ∠EFG = 180°
From the given diagram, ∠EFG = 110°
Then,
2 × ∠FEG + 110° = 180°
2 × ∠FEG = 180° - 110°
2 × ∠FEG = 70°
∠FEG = 70° ÷ 2
∠FEG = 35°
Hence, the measure of ∠FEG (m∠FEG) is 35°. The correct option is the third option m∠FEG = 35°
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