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Question
In the given figure, if AB || HF and DE || FG, then the measure of ∠FDE is
Options
108°
80°
100°
90°
Solution
The given figure is as follows:
It is given that . AB || HF
Thus, x and ∠HFC form a linear pair, therefore,
∠HFC + x = 180°
28° + = 180°
x = 180° - 28°
x = 152° (1)
Also ED || GF
Thus, x and ∠FDB are corresponding interior opposite angles, therefore,
∠FDB = x
y + 72° = x
y = x - 72°
From (i):
y = 152° - 72°
y = 80°
Thus, ∠FDE = 80°
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