The sides BC, CA and AB of ∆ABC have been produced to D, E and F, respectively. ∠BAE + ∠CBF + ∠ACD = ?
(a) 240°
(b) 300°
(c) 320°
(d) 360°

Open in App

Solution

(d) 360°

We have :
$∠ 1 + ∠ B A E = 180 ° . . . (i) ∠ 2 + ∠ C B F = 180 ° . . . (i i) and ∠ 3 + ∠ A C D = 180 ° . . . (i i i)$
$Adding (i), (i i) and (i i i), we get: (∠ 1 + ∠ 2 + ∠ 3) + (∠ B A E + ∠ C B F + ∠ A C D) = 540 °$
$\Rightarrow 180 ° + ∠ B A E + ∠ C B F + ∠ A C D = 540 ° [∵ ∠ 1 + ∠ 2 + ∠ 3 = 180 °] \Rightarrow ∠ B A E + ∠ C B F + ∠ A C D = 360 °$

Suggest Corrections

Similar questions

$The sides BC,CA and AB of Δ A B C have been produced to D ,E and respectively ∠ B A E + ∠ C B F + ∠ A C D = ? .$

$(a) 240^{\circ} (b) 300^{\circ} (c) 320^{\circ} (d) 360^{\circ}$

Sides BC, CA and AB of a triangle ABC are produced in an order, forming exterior angles ∠ACD, ∠BAE and ∠CBF. Show that ∠ACD + ∠BAE + ∠CBF = 360°.

The sides BC, CA and AB of $Δ A B C$ are produced in order to form exterior angles $∠ A C D$ , $∠ E A B$ , and $∠ C B F$ .

Find $∠ A C D + ∠ C B F + ∠ E A B$ .

B C, C A

A B

△ A B C

D, E

F

∠ A C D = 105^{o}

∠ E A F = 45^{o}

△ A B C

Join BYJU'S Learning Program