In a triangle ABC, the angle bisector of ∠A meets BC at D. The angle bisector of ∠C meets AB at E. AD and CE intersect at point I. ∠B = 80°. Find ∠AIC.
Show Worked Solution
Worked Solution
Step 1: I is the incentre of triangle ABC (intersection of angle bisectors).
Step 2: A standard incentre-angle theorem: ∠AIC = 90° + (∠B)/2.
Step 3: ∠AIC = 90° + 80°/2 = 90° + 40° = 130°.
Answer: 130°
Correct answer: 130°
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