If the bisectors of the acute angles of a right triangle meet at `O ,` then the angle at `O` between the two bisectors is `45^0` (b) `95^0` (c) `135^0` (d) `90^0`

Explanation

Let ABC is an acute angled triangle.` /_B = 90@`
We know that,` /_A + /_B + /_C = 180@
/_A + 90@ +/_C = 180@
/_A + /_C = 90
.....(i) In ΔAOC /_AOC + /_ACD + /_CAD = 180@
/_AOC + 1 /2 (/_A+∠C ) = 180@
∠AOC + 1/ 2 ( 90@) = 180@`[From (i)] `∠AOC + 45@ = 180@
∠AOC = 180@ – 45@ = 135@`