Observe the given construction, AF is the angular bisector of ∠BAE and AC is the angular bisector of ∠BAF. If ∠BAE = 60⁰, then find the measurement of ∠BAC.

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Solution

∠BAE = 60⁰ [Given]
AF is angle bisector of ∠BAE
=> ∠BAF = (1/2) ∠BAE = (1/2) * 60⁰ = 30⁰, and
AC is angle bisector of ∠BAF
=> ∠BAC = (1/2) ∠BAF =(1/2) * 30⁰ = 15⁰

Hence, ∠BAC = 15⁰.

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