Question

in triangle ABC the angle A=60 degree, angle b= 80 degree and the bisectors of Angle B and angle C meet at O.
find:

(i) angle C
(it) angle BOC

answer with method ​

Answer 1

In Triangle ABC ,

<A + < B + < C = 180⁰ ( Angle sum property of a triangle)

80⁰ + 60⁰ + < c = 180⁰

< C = 40⁰

Now, since OC is the bisector of <C ,

Also , OB is the bisector of < B ,

Therefore , < OCB =20⁰ & < OBC = 40⁰

In triangle OBC ,

< OBC + < OCB + < BOC = 180⁰ ( ANGLE SUM PROPERTY)

Therefore , < BOC = 180 ⁰ - (40⁰ +20⁰)

=> 180⁰-60⁰

=> 120⁰

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Answer 2

Answer:

(i) 40

(ii)240 or 120

Step-by-step explanation:

(i) ∆ABC,

A+B+C=180

60+80+C=180

C=40

(ii) because of bisectors,

/_ABO=(1/2)B

=(1/2)80

=40

/_ACO=(1/2)C

=(1/2)40

=20

so,

A+B+O+C=360

60+40+O+20=360

O=240(outer triangle)(inner square)

in triangle,

∆OBC= O+B+C=180

/_BOC=180-40-20

=120