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In the figure given below, if BA || FH and ED || GF, then what is the measure of $∠ F D E$ ?

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80 °

100 °

40 °

30 °

answer is A.

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Detailed Solution

It is given that

B A ∥ F H

and

E D ∥ G F .

In the figure, if AB||HF and DE||FG, then the measure of ∠ FDE is

Since the lines BA || FH, and CD is a transversal, therefore using the corresponding angle property, we have,

∠ H F C = ∠ F D A ⇒ ∠ F D A = 28 °

Using the property of linear pair, we have,

∠ F D A + ∠ F D E + ∠ E D B = 180 °

⇒ 28 ° + ∠ F D E + 72 ° = 180 ° ⇒ 100 ° + ∠ F D E = 180 ° ⇒ ∠ F D E = 180 ° − 100 ° ⇒ ∠ F D E = 80 °

Therefore, the measure of

∠ F D E = 80 ° .

Hence, option (1) is correct.

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