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Question
If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.
Solution
Given the bisectors the base angles of an triangle enclose an angle of `135^@`
i.e., ∠BOC=`135^@`
But, W.K.T
`∠ BOC=90^@+1/2∠B`
⇒ `135^@=90^@+1/2∠A`
⇒`1/2∠A=135^@-90^@`
⇒`∠A=45^@(2)`
⇒`∠A=90^@`
∴ ΔABC is right angled triangle right angled at A.
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