Math, asked by shakyajaydevi82, 7 months ago

in triangle a B c is a bisecter of angleb and c interest at o then measure the angle boc

Answers

Answered by anushrirastogi1234

Answer:

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Step-by-step explanation:

ABC is a triangle in which A=60°, bisectors of angles B and C meet at point O.

In triangle ABC

60°+B+C=180°. or. B+C=120°…………….(1)

B0 is bisector of. angle B and CO is bisector of angle C . Thus

angle OBC=B/2. , angle. OCB = C/2.

In triangle OBC

angle BOC+ angle OBC. + angle OCB. =180°

angle BOC. +B/2 +C/2=180°

angle BOC = 180°- 1/2(B+C). Putting B+C=120° from eqn.(1)

angle BOC. = 180°-1/2(120°) = 180°-60°. = 120°. Answer.

In triangle ABC the angle bisector of angle B and angle C meet at point O. Can you find the measure of angle BOC?

Angle A is 80° and is the bisector to the interior angles, angle B and angle C meet at O. What is angle BOC?

What is the measure of ∠BOC if in a ΔABC the internal bisector of ∠B and ∠C meet at O & ∠A = 72⁰?

ABCD is a quadrilateral, AO and BO are the bisectors of angle A and B which meet at O.What is the angle of AOB If angle C =70° and angle D=50°?

In ΔABC, AB = AC and the bisector of angles B and C intersect at point O. Prove that BO = CO and AO bisects ∠BAC?

In a triangle, the sum of total angle =180°

Thus in ∆ABC, ∠A+∠B+∠C=180°

⇒60°+∠B+∠C=180°

⇒∠B+∠C=180°−60°=120°

⇒∠B+∠C2=120°2

⇒∠B2 +∠C2=60°

⇒∠OBC+∠OCB=60°

Thus, in ∆OBC, ∠OBC+∠OCB+∠BOC=180°

⇒∠BOC=180°−60°=120°

Happy math!!

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120 degrees.

In triangle ABC, angle A = 60 degrees. and let angle B = 2b and angle C = 2c.

Thus 60 + 2b + 2c = 180 degrees, or

2b + 2c = 180 - 60 - 120 degrees, or

b + c = 60 degrees.

In triangle OBC, angle BOC +angle OBC + angle OCB = 180 degrees.

But angle OCB +angle OBC = b + c = 60 degrees, so

angle BOC +angle OBC + angle OCB = 180 degrees, or

angle BOC +60 = 180 degrees, therefore

angle BOC = 120 degrees.

Angle BOC = 120

PROOF

Angle A + Angle B + Angle C = 180

So, Angle B + Angle C = 120 ( angle A = 60)

Now 1/2 (Angle B + Angle C) = 60

1/2 angle B + 1/2 angle C =60………. I

In triangle BOC

1/2 angle B + 1/2 angle C + Angle BOC = 180

(BO and CO are angle bisectors)

Or 60 + Angle BOC = 180 (Using I)

OR ANGLE BOC = 120

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In triangle ABC, angle ABC is 90 degrees and angle BAC is 60. If the bisector of angle BAC meets BC at D, then what is BD:DC?

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Below mentioned are the long methods i guess,

i tried with given below method i found some where you can try that :

⇒ ∠BOC = 90 + 1/2 (given angle) ;

⇒ ∠BOC = 90 + 1/2 (60);

⇒ ∠BOC = 90 + 30;

⇒ ∠BOC = 120;

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It can easily be proved that angle BOC is equal to 90 + A/2. So angle BOC = only depends on angle A.