Question

In a ΔABC, ∠A = 103°, ∠B = 42°. The bisectors of angles B and C meet at I. Find ∠BIC. Also, the

bisectors of the external angles B and C meet at E. Find ∠BEC.​

Answer 1

Step-by-step explanation:

In triangle ABC

Using Angle Sum Property, angleA + angleB + angleC = 180

Since angleA = 70, angleB + angleC = 110 →(i)

In triangle BOC

Using Angle Sum Property, angleBOC + angleOCB + angleOBC = 180

angleBOC + 1/2angleC + 1/2angleB = 180

angleBOC + 1/2(angleC + angleB) = 180

angleBOC + 1/2(110) = 180

angleBOC = 180-55

angleBOC = 125

Alter method: Using Corrolary of Angle Sum Property

angleBOC = 90 + 1/2angleA

angleBOC = 90 + 35

angleBOC = 125

Answer 2

Answer:

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