Geometry Practice Test 1

Question : 17 of 40

Marks: +1, -0

I is the incentre of a triangle ABC. If ∠ABC = 65° and ∠ACB = 55°, then the value of ∠BIC is:

Solution:

I is the incenter of ΔABC.
∠ABC = 65°
∠ACB = 55°

∠BIC = x°
∠1 = ∠2 and ∠3 = ∠4
∠1 + ∠2 + ∠3 + ∠4 = 65° + 55°
2∠2 + 2∠3 = 120°
∠2 + ∠3 =

{120°}/2

= 60°
Now ∠BIC+∠2 +∠3 = 180°
∠BIC = 180° − 60° = 120°

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