If the bisectors of the base angles of a triangle enclose an angle of 135 degree,prove that the triangle is a right triangle.
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Answered by
328
hi dear friend.
let the bisectors of the base angles B and C of trianle ABC meet at O.
given angle BOC = 135
In triangle BOC
OBC+BOC+OCB=180
1/2B+135+1/2C=180
1/2(B+C)=180-135=45
B+C=45*2=90-----i
In triangleABC
A+B+C=180
A=180-(B+C)
A=180-90=90
A=90
Therefore triangle ABC is an right triangle
hope it helps uh ;)
let the bisectors of the base angles B and C of trianle ABC meet at O.
given angle BOC = 135
In triangle BOC
OBC+BOC+OCB=180
1/2B+135+1/2C=180
1/2(B+C)=180-135=45
B+C=45*2=90-----i
In triangleABC
A+B+C=180
A=180-(B+C)
A=180-90=90
A=90
Therefore triangle ABC is an right triangle
hope it helps uh ;)
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75
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