Three straight lines, $X, Y a n d Z$ are parallel and the angles are as shown in the figure below. What is $∠ A F B$ equal to?

20^{\circ}

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15^{\circ}

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30^{\circ}

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10^{\circ}

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Solution

The correct option is B $15^{\circ}$
$∠ C D E = 180^{\circ} - 125^{\circ} = 55^{\circ} I n Δ D C E, ∠ C E D = 180^{\circ} - 55^{\circ} - 80^{\circ} = 45^{\circ}$
$a n d ∠ A B F = 30^{\circ}$ (vertically opposite)
Also, $∠ A B F = ∠ B F M = 30^{\circ}$ (alternate angle)
and, $∠ D E F = ∠ E F M$ (alternate angle )
$∠ E F M = 45^{\circ}$
$\Rightarrow ∠ E F B + ∠ B F M = 45^{\circ} \Rightarrow ∠ E F B = 45^{\circ} - 30^{\circ} \Rightarrow ∠ A F B = 15^{\circ}$

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Three straight lines, X,Y and Z are parallel and the angles are as shown in the figure below. What is ∠AFB equal to?

The correct option is B 15∘∠CDE=180∘−125∘=55∘In ΔDCE,∠CED=180∘−55∘−80∘=45∘ and ∠ABF=30∘ (vertically opposite) Also, ∠ABF=∠BFM=30∘ (alternate angle) and, ∠DEF=∠EFM (alternate angle ) ∠EFM=45∘ ⇒∠EFB+∠BFM=45∘⇒∠EFB=45∘−30∘⇒∠AFB=15∘

Three straight lines, $X, Y a n d Z$ are parallel and the angles are as shown in the figure below. What is $∠ A F B$ equal to?