Q. 123.7( 3 Votes )

If the bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is
A. 45°

B. 95°

C. 135°

D. 90°

Answer :

Let ABC is an acute angled triangle.

B = 90o


We know that,


A + B + C = 180o


A + 90o + C = 180o


A + C = 90o (i)


In


AOC + ACD + CAD = 180o


AOC + C + A = 180o


AOC + (A + C) = 180o


AOC + * 90o = 180o [From (i)]


AOC + 45o = 180o


AOC = 180o – 45o


= 135o


Thus, the angle at O between two bisectors is equal to 135o.

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