In the following figure, FD∥BC∥AE and AC∥ED. Find the value of x.

Question

In the following figure,

F D ∥ B C ∥ A E

and

A C ∥ E D

. Find the value of x.

Answer:
:

Δ A B C

∠ A B C + ∠ B C A + ∠ C A B = 180^{\circ}

[Angle sum property of triangle]

\Rightarrow 64^{\circ} + ∠ B C A + 52^{\circ} = 180^{\circ}

\Rightarrow ∠ B C A = 180^{\circ} - 64^{\circ} - 52^{\circ} = 64^{\circ}

∠ F A E = ∠ B C A

[

∵

Alternate angles;

A E ∥ B C

, AC is the transversal]

\Rightarrow ∠ F A E = 64^{\circ}

Now,

∠ F A E + x = 180^{\circ}

[Adjacent angles in a parallelogram are supplementary]

\Rightarrow x = 180^{\circ} - 64^{\circ} ∴ x = 116^{\circ}

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