Question

In Δ ABC, if ∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at a point O, then find the measure of ∠BOC.

Answer 1

The measure of ∠BOC = 110°.

Step-by-step explanation:

Given data:

In ΔABC, ∠B = 60°, ∠C = 80°

The bisectors of angles ∠ABC and ∠ACB meet at O.

Since BO is the bisector of ∠B.

$\angle \mathrm{OBC}=\frac{1}{2}\angle B$

          $=\frac{1}{2}\left(60^{\circ}\right)$

          = 30°

∠OBC = 30°

Similarly, OC is the bisector of ∠C.

$\angle \mathrm{OCB}=\frac{1}{2}\angle C$

          $=\frac{1}{2}\left(80^{\circ}\right)$

          = 40°

∠OCB = 40°

In ΔBOC,

Angle sum property of triangle,

$\angle \mathrm{OCB}+\angle \mathrm{OBC}+\angle \mathrm{BOC}=180^{\circ}$

$30^{\circ}+40^{\circ}+\angle \mathrm{BOC}=180^{\circ}$

$\angle \mathrm{BOC}+70^{\circ}=180^{\circ}$

$\angle \mathrm{BOC}=180^{\circ}-70^{\circ}$

$\angle \mathrm{BOC}=110^{\circ}$

The measure of ∠BOC = 110°.

To learn more...

1. In the figure , sides AB and AC of triangle ABC are produced to point E and D respectively . if bisectors BO and CO of angle CBE and angle BCD respectively meet at point O, then prove that angle BOC =90°-1/2 angle BAC .

https://brainly.in/question/1350103

2. In triangle abc  ,if angle b = 60° angle c =80° and the bisectors of an angles triangle ABC and ACB  meet at point o, then find the measure of  angle BOC

https://brainly.in/question/33720

Answer 2

Answer:

answer is 110°

Step-by-step explanation:

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