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 $∠ A C D + ∠ C B F + ∠ E A B$ .

$180^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$270^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$360^{\circ}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$540^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$360^{\circ}$

Sum of angles in a triangle is 180 $^{\circ}$ , So

$x + y + z = 180^{\circ}$

$∠ A C D + ∠ C B F + ∠ E A B$ = $(180^{\circ} - z) + (180^{\circ} - x) + (180^{\circ} - y)$

= $540^{\circ} - (x + y + z)$

= $540^{\circ} - 180^{o}$

= $360^{\circ}$

Suggest Corrections

Similar questions

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 $∠ C B F$ . If $x + y + z = 180^{\circ}$ then $∠ A C D + ∠ C B F + ∠ E A B$ is

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°.

Q. The sides BC, CA and AB of

Δ A B C

are produced in order to form exterior angles

∠ A C D

∠ B A F

and

∠ C B E

respectively, then

∠ B A F + ∠ A C D + ∠ C B E

is ______ degree(s).

The sides AB, CA and AB of triangle ABCare produced in order to form exterior angles ACD, FBA,and angle CAE then angle ACD+CAE+ABF is

Q. The sides BC, CA and AB of ∆ABC have been produced to D, E and F, respectively, as shown in the figure, forming exterior angles ∠ACD, ∠BAE and ∠CBF. Then, ∠ACD + ∠BAE + ∠CBF = ?
(a) 240°
(b) 300°
(c) 320°
(d) 360°

Join BYJU'S Learning Program

The sides BC, CA and AB of ΔABC are produced in order to form exterior angles ∠ACD , ∠EAB, and ∠CBF. Find ∠ACD+∠CBF+∠EAB.

The correct option is C 360∘ Sum of angles in a triangle is 180∘, So x+y+z=180∘ ∠ACD+∠CBF+∠EAB = (180∘−z)+(180∘−x)+(180∘−y) = 540∘−(x+y+z) = 540∘−180o = 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 $∠ A C D + ∠ C B F + ∠ E A B$ .

The correct option is C
$360^{\circ}$

Sum of angles in a triangle is 180 $^{\circ}$ , So

$x + y + z = 180^{\circ}$

$∠ A C D + ∠ C B F + ∠ E A B$ = $(180^{\circ} - z) + (180^{\circ} - x) + (180^{\circ} - y)$

= $540^{\circ} - (x + y + z)$

= $540^{\circ} - 180^{o}$

= $360^{\circ}$