Question

O. Is the centre of the circle angle Aob is 60 and angle cdb is 90 find angle obc

Answer 1

Answer: angle AOD =60°

angle DCB =30° ( by angle sustended theroem)

angle (DCB+OBC+BDC) = 180°(A.S.P of a triangle)

30° + 90° + OBC = 180°

OBC = 180° - 120°

OBC = 60°

i hope this helps you

Answer 2

Given:

O is the center of the circle.

∠AOB is 60°

∠CBD is 90°

To Find:

∠OBC

Solution:

∠AOB = 60° (given)

∠CDB = 90°  (given)

∠ DCB = 30°   ( angle extended theorem)

∠DCB + ∠OBC + ∠BDC = 180°  (angle sum property of a triangle)

 30° + 90° + ∠OBC = 180°

 120° + ∠OBC = 180°

     ∠OBC = 180° - 120°

     ∠OBC = 60°

Therefore, the ∠OBC = 60°