You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Vertically Opposite Angles

Find x and ...

Question

Find $x$ and $y$ if $B D$ and $C D$ are angle bisectors

Open in App

Solution

$Δ A B C$
$∠ A + ∠ B + ∠ C = 180^{\circ}$ (by angle sum property)
$\Rightarrow 80^{\circ} + 2 x + 60^{\circ} = 180^{\circ}$
$\Rightarrow 2 x = 180^{\circ} - 140^{\circ}$
$\Rightarrow 2 x = 40^{\circ}$
$\Rightarrow x = 20^{\circ}$
In $Δ B D C$
$∠ B + ∠ D + ∠ C = 180^{\circ}$
$\Rightarrow x + y + 30^{\circ} = 180^{\circ}$
$\Rightarrow 20^{\circ} + y + 30^{\circ} = 180^{\circ}$
$\Rightarrow y = 180^{\circ} - 50^{\circ}$
$\Rightarrow y = 130^{\circ}$
So , $x = 20^{\circ}, y = 130^{\circ}$

Suggest Corrections

Similar questions

Q. In the adjoining figure, BD and CD are angle bisectors. Then, which of the following is true ?

Q. The straight lines

A B

and

C D

intersect at

E

. If

E F

and

E G

are bisectors of

∠ D E A

and

∠ A E C

respectively and if

∠ A E F = x

and

∠ A E G = y

, then

Q. In the adjoining figure,

B D

and

C D

are angle bisectors of

∠ A B C

and

∠ A C E

respectively(Line BC is extended to E). Then, which of the following is true?

Q. If

∠ A = 100^{\circ}

, AB = AC, CD bisects

∠ A C B

and BD bisects

∠ A B C

. The values of x and y are

In given figure $∠ X = 62^{\circ}, ∠ X Y Z = 54^{\circ}$ . If $Y O$ and $Z O$ are the bisectors of $∠ X Y Z$ and $∠ X Z Y$ respectively of $Δ X Y Z$ . Find $∠ O Z Y$ and $∠ Y O Z$ .

Join BYJU'S Learning Program

Find x and y if BD and CD are angle bisectors

ΔABC ∠A+∠B+∠C=180∘ (by angle sum property)⇒80∘+2x+60∘=180∘⇒2x=180∘−140∘⇒2x=40∘⇒x=20∘In ΔBDC∠B+∠D+∠C=180∘⇒x+y+30∘=180∘⇒20∘+y+30∘=180∘⇒y=180∘−50∘⇒y=130∘So , x=20∘,y=130∘

Find $x$ and $y$ if $B D$ and $C D$ are angle bisectors