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

Open in App

Solution

By angle sum property,
$x + y + z = 180^{\circ}$
$∠ B A F + ∠ A C D + ∠ C B E$
$= (180^{\circ} - x) + (180^{\circ} - y) + (180^{\circ} - z)$
$= 540^{\circ} - (x + y + z) = 540^{\circ} - 180^{\circ} = 360^{\circ}$

Suggest Corrections

Similar questions

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

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).

Q. Sides BC, AB and CA of ΔABC are extended to D, E and F respectively. CG, BG, CH, AH, BI and AI are bisectors of ∠ACD, ∠ABC, ∠ACB, ∠BAF, ∠CBE and ∠BAC respectively, then sum of angles ∠BGC, ∠AHC and ∠AIB is

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

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

Join BYJU'S Learning Program

The sides BC, CA and AB of ΔABC are produced in order to form exterior angles ∠ACD, ∠BAF and ∠CBE respectively, then ∠BAF+∠ACD+∠CBE is

By angle sum property, x+y+z=180∘ ∠BAF+∠ACD+∠CBE =(180∘−x)+(180∘−y)+(180∘−z) =540∘−(x+y+z)=540∘−180∘=360∘

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

By angle sum property,
$x + y + z = 180^{\circ}$
$∠ B A F + ∠ A C D + ∠ C B E$
$= (180^{\circ} - x) + (180^{\circ} - y) + (180^{\circ} - z)$
$= 540^{\circ} - (x + y + z) = 540^{\circ} - 180^{\circ} = 360^{\circ}$