Question

in abc right angled at b from the other two angles one angle is twice of the other angle the bisector of right angle and the larger acute angle meet at a point o then find the angle between two bisector​

Answer 1

Given: ABC is the right angle triangle, the right angle will be formed at B.

AO and OC are the angle bisectors of

ZBAC and <BCA

To Find That:

ZAOC

Solution:

Since AO and OC are the angle bisectors of ZBAC and ZBCA

ZOAC = 1/2 <BAC - (1)

ZOCA = 1/2 <BCA - (2)

Now we will add equation 1 and 2

ZOAC + ZOCA = 1/2 ZBAC + 1/2/BCA

= 1/2(2BAC + <BCA)

= 1/2 (180-2ABC)

(the sum of interior angles is 180 degrees)

ZOAC + ZOCA = 1/2 [180-90]

= 1/2 * 90

= 45