From the given figure evaluate the value of x if AB is parallel to CD and the line t is a transversal.

$30^{\circ}$

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$20^{\circ}$

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$22^{\circ}$

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$25^{\circ}$

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Solution

The correct option is B
$20^{\circ}$

$∠ C F E = 5 x (V e r t i c a l l y o p p o s i t e a n g l e s)$ ..... (i)

$∠ A E F = 4 x (G i v e n)$ ...(ii)

$∠ C F E + ∠ A E F = 180^{\circ} (C o - i n t e r i o r a n g l e s)$ ......(iii)

$5 x + 4 x = 180^{\circ}$ ..From eq (i) and (ii)

$9 x = 180^{\circ}$

$x = 20^{\circ}$

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From the given figure evaluate the value of x if AB is parallel to CD and the line t is a transversal.

The correct option is B 20∘ ∠CFE=5x (Vertically opposite angles)..... (i) ∠AEF=4x (Given)...(ii) ∠CFE+∠AEF=180∘ (Co−interior angles)......(iii) 5x+4x=180∘ ..From eq (i) and (ii) 9x=180∘ x=20∘