In a ΔABC, ∠A = 103°, ∠B = 42°. The bisectors of angles B and C

1.	In a ΔABC, ∠A = 103°, ∠B = 42°. The bisectors of angles B and C meet at I. Find ∠BIC. Also, thebisectors of the external angles B and C meet at E. Find ∠BEC.
Answer» 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

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

Answer»

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