Find - ABF from the given figure-A- 30-B- 45-C- 75-D- 60-

The correct option is D 60º ∠ BCD + ∠ BCH = 180^∘ [ Linear pair] ∠ BCD = 180^∘ 35^∘ = 145^∘ In quadrilateral BEDC, ∠ BED + ∠ EDC + ∠ DCB + ∠ CBE = 360^∘ ∠ ...

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Byju's Answer

Standard VIII

Mathematics

Sum of Interior Angles in a Polygon

Find ∠ ABF fr...

Question

Find $∠ A B F$ from the given figure.

30º

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45º

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60º

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75º

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Solution

The correct option is C
60º

$∠ B C D + ∠ B C H = 180^{\circ}$ [ Linear pair]
$∠ B C D$ = $180^{\circ}$ - $35^{\circ}$ = $145^{\circ}$
In quadrilateral BEDC, $∠ B E D$ + $∠ E D C$ + $∠ D C B$ + $∠ C B E$ = $360^{\circ}$
$∠ C B E$ = $360^{\circ}$ - ( $105^{\circ}$ + $50^{\circ}$ + $145^{\circ}$ ) = $60^{\circ}$
So, $∠ A B F$ = $∠ C B E$ = $60^{\circ}$ (Vertically opposite angles)

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Find ∠ABF from the given figure.

The correct option is C 60º ∠BCD+∠BCH=180∘ [ Linear pair] ∠BCD = 180∘ - 35∘ = 145∘ In quadrilateral BEDC, ∠BED + ∠EDC + ∠DCB + ∠CBE = 360∘ ∠CBE = 360∘ - (105∘ + 50∘ + 145∘) = 60∘ So, ∠ABF = ∠CBE = 60∘(Vertically opposite angles)

Find $∠ A B F$ from the given figure.