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In the below figure, if $A B ‖ D E$ and $B D ‖ F G$ such that $∠ F G H = 125 °$ and $∠ B = 55 °$ , the value of x and y is:

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x = 70° and y = 55°.

x = 50° and y = 45°.

x = 20° and y = 45°.

x = 80° and y = 25°.

answer is A.

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Detailed Solution

Given a figure in which

A B ‖ D E

and

B D ‖ F G

such that

∠ F G H = 125 °

and

∠ B = 55 °

In the given figure, if A B D E and B D F G such that ∠ F G H=125∘ and ∠ B= 55∘, find x and y.

As we know that, alternate interior angles are equal.
Therefore,

∠ D = ∠ B ⇒ ∠ D = 55 ° … … . (1)

Also, BD || FG and having transversal DF, so alternate interior angles are equal.

∠ D = ∠ F ⇒ ∠ F = 55 ° [From eq 1]

Linear pair property states that the sum of angles of a linear pair is always equal to 180°.
Using linear pair property,

∠ F G E + ∠ F G H = 180 ° ⇒ y + 125 ° = 180 ° ⇒ y = 180 ° − 125 ° ⇒ y = 55 °

Exterior angle property states that if a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Using exterior angle property,

E x t . ∠ F G H = ∠ F + ∠ E ⇒ 125 ° = 55 ° + x ⇒ x = 125 ° − 55 ° ⇒ x = 70 °

Hence, the value of

x = 70 ° a n d y = 55 °

.
Hence, option 1 is correct.

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