ABC is a triangle in which ∠ A = 72°, the internal bisectors of angles B and C meet in O . Find the magnitude of ∠ BOC .

Question

ABC is a triangle in which &#x2220; A = 72&#xB0;, the internal bisectors of angles B and C meet in O . Find the magnitude of &#x2220; BOC .

Philoid · Accepted Answer

Given,

ABC is a triangle

∠A = 72^o and internal bisectors of B and C meet O.

In

∠A + ∠B + ∠C = 180^o

72^o + ∠B + ∠C = 180^o

∠B + ∠C = 180^o – 72^o

∠B + ∠C = 108^o

Divide both sides by 2, we get

+ =

+ = 54^o

∠OBC + ∠OCB = 54^o (i)

Now, in

∠OBC + ∠OCB + ∠BOC = 180^o

54^o + ∠BOC = 180^o [Using (i)]

∠BOC = 180^o – 54^o

= 126^o