In - PQR- the angle bisectors of - PQR and - PRQ meet at O-If - QPR - 80- - find the measure of- QOR-

∠ 1 = ∠ 2 = 1/2∠ Q (OQ bisects ∠ PQR) nbsp; ⇒∠ Q = 2 ∠ 2 ∠ 3 = ∠ 4 = 1/2∠ R (OR bisects ∠ PRQ) ⇒∠ R = 2 ∠ 3 In Δ PQR, 80^∘+∠ Q+∠ R=180^∘ ⇒∠ Q+∠ R=100^∘ ⇒ ...

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

Byju's Answer

Other

Quantitative Aptitude

Lines and Angles

In Δ PQR, the...

Question

$In Δ P Q R, the angle bisectors of ∠ P Q R and ∠ P R Q meet at O.$

$If ∠ Q P R = 80^{\circ}, find the measure of ∠ Q O R$ .

Open in App

Solution

$∠ 1 = ∠ 2 = \frac{1}{2} ∠ Q (OQ bisects ∠ P Q R$ )
$\Rightarrow ∠ Q = 2 ∠ 2$
$∠ 3 = ∠ 4 = \frac{1}{2} ∠ R (OR bisects ∠ P R Q$ )
$\Rightarrow ∠ R = 2 ∠ 3$
$In Δ P Q R, 80^{\circ} + ∠ Q + ∠ R = 180^{\circ}$
$\Rightarrow ∠ Q + ∠ R = 100^{\circ}$
$\Rightarrow 2 ∠ 2 + 2 ∠ 3 = 100^{\circ}$
$\Rightarrow 2 (∠ 2 + ∠ 3) = 100^{\circ}$
$\Rightarrow ∠ 2 + ∠ 3 = 50^{\circ}$
$In Δ Q O R, ∠ 2 + ∠ 3 + ∠ Q O R = 180^{\circ} \Rightarrow 50^{\circ} + ∠ Q O R = 180^{\circ}$
$\Rightarrow ∠ Q O R = 180^{\circ} - 50^{\circ} = 130^{\circ}$

Suggest Corrections

Similar questions

Q. In

Δ P Q R

, the angle bisectors of

∠ P Q R

and

∠ P R Q

meet at O.

∠ Q P R = 80^{\circ}

, find the measure of

∠ Q O R

Q. In the given quadrilateral

O Q P R,

∠ Q P R = 50^{\circ}

then

∠ Q O R

equals

In a triangle ABC, $∠ A = 60^{\circ}$ and the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively.

Q. In a

△ P Q R

the angle bisectors of

∠ P Q R

and

∠ P R Q

meet t O. If

∠ Q P R = 80^{o}

, what is the measure of

∠ Q O R

In the following figure, PQ and PR are tangents to the circle, with centre O. If $∠ Q P R = 60^{o}$ , calculate :

(i) $∠ Q O R,$
(ii) $∠ O Q R,$
(iii) $∠ Q S R,$

Join BYJU'S Learning Program

In ΔPQR,the angle bisectors of ∠PQR and ∠PRQ meet at O. If ∠QPR=80∘,find the measure of∠QOR.

$In Δ P Q R, the angle bisectors of ∠ P Q R and ∠ P R Q meet at O.$

$If ∠ Q P R = 80^{\circ}, find the measure of ∠ Q O R$ .