What is the value of FG?
and are parallel Then, what is the value of ?
The answer is 30.
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1 solution
Let ∠CFD = θ and ∠CDF = β (since it is not given if it is right angle or not).
Since FD and EG is parallel, then ∠CFD = ∠CGE and ∠CDF = ∠CEG.
Using sine law for angles: (sin β) / b = (sin θ) / CD (sin β) / (5 + x) = (sin θ) / (CD + a)
Equating values for sin β:
bsinθ / CD = sin β = (5+x)sinθ / (CD + a)
b / CD = (5+x) / (CD + a), eliminating sin θ
5 / 1 = (5 +x) / 7
(5)(7) = 5 + x
35 = 5 + x
x = 35 - 5 = 30