Question

In the given figure , if AOD = 135 then BOC is equal to what
a)52.5

b)45

c)62.5

d)24

Answer 1

it is 45 as aod+boc=180 as it is a known theorm

Answer 2

Mark the angles a, x and y.  Then find the other angles, because we have right angle triangles.  Also we have identical triangles, as the sides are tangents from A , B C and D  on to the circle.   So the lengths of tangent segments on to the circle are equal.   Thus the angles inside the two adjacent triangles are equal.

  Sum of all angles at the center = 360 deg

     135-a + 135-a + a + a + 2 x + 2 y = 360 deg
  
       2x + 2y = 90 deg
 
        x + y = 45 deg =  angle BOC.