LAOB = 130°, LAOD = 20°, <COD = 45°, <COB - ?

To find the angle <COB, we can use the information given about the angles around point O.

Given:

• \( \angle LAOB = 130^\circ \)
• \( \angle LAOD = 20^\circ \)
• \( \angle COD = 45^\circ \)

We can determine <COB using the relationship between these angles.

1. First, calculate \( \angle AOD \):

   • Since \( \angle LAOB \) can be broken down into \( \angle LAOD \) and \( \angle AOB \): \[ \angle AOB = \angle LAOB - \angle LAOD = 130^\circ - 20^\circ = 110^\circ \]

2. Now apply the full circle (360 degrees) around point O: \[ \angle AOB + \angle COD + \angle COB + \angle LAOD = 360^\circ \] So, rearranging this for \( \angle COB \): \[ \angle COB = 360^\circ - (\angle AOB + \angle COD + \angle LAOD) \] Substituting the known values: \[ \angle COB = 360^\circ - (110^\circ + 45^\circ + 20^\circ) \] \[ \angle COB = 360^\circ - 175^\circ \] \[ \angle COB = 185^\circ \]

Therefore, \( \angle COB = 185^\circ \).