Question

In ΔABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. The measure of ∠BOC is

Answer 1

Answer:

Lines and Angles

In ∆ABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. The measure of ∠BOC is: 40°

Answer 2

Answer:

In the triangle the measure of  ∠BOC is 65

Step-by-step explanation:

Given: In ΔABC, ∠A = 50°

To find: To find the measure of ∠BOC

Solution:

Let us consider a triangle ABC

The bisector ∠B and ∠C meet at O in the figure.

Given that  ∠A is equal to 50∘ and it is a interior angle.

Therefore the exterior angle is given by subtracting it from 180 as the angle formed by straight line is 180

⇒ ∠A =180−50

∠A =130

We know that

The sum of the exterior angles of any closed figure is 360

⇒ ∠A + ∠B + ∠C = 360

Sub ∠A =130

⇒ 130 + ∠B + ∠C = 360

⇒ ∠B + ∠C = 360 - 130

⇒ ∠B + ∠C = 230

Let us consider the triangle ΔBOC

Hence ∠B  is bisected then we get ∠BOC = ∠B / 2

           ∠C  is bisected then we get ∠OCB = ∠C / 2

We know that sum of the angles of the triangle is 180

⇒ ∠0BC + ∠OCB + ∠BOC = 180

⇒ ∠B/2 + ∠C/2 + ∠BOC = 180

⇒ (∠B+ ∠C)/2 + ∠BOC = 180

∠B + ∠C = 230

⇒ 230/2 + ∠BOC = 180

⇒ 115 + ∠BOC = 180

⇒ ∠BOC = 180 - 115

⇒ ∠BOC = 65

In a triangle, the lengths of the first two sides are always bigger than the length of the third side.

The measure of  ∠BOC = 65

Final answer:

In the triangle the measure of  ∠BOC is 65

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