In ∆ABC,B=35° and C=65°and the bisectors of angle BAC meets BC at X.Arrange AX,BX and CX in their decreasing order

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Solution

In triangle ABC,
<A + <B + <C = 180
<A + 35 + 65 = 180
<A + 100 = 180
<A = 180 - 100 = 80

So, <BAX = <CAX = 80/2 = 40

we know that: side opposite to bigger angle is longer

In triangle BAX,
<BAX (40o) > <ABX (35o)
so, BX > AX

In triangle CAX,
<ACX (65o) > <CAX(40o)
so, AX > CX

so, BX > AX > CX

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