Based on the image, find the value of angle COD if angle AOB = 123 degrees and angle AOD = 98 degrees. Angle AOC = 90 degrees.

Let's solve this geometry problem step by step. 1. Understanding the Problem: * We are given \(\angle AOB = 123^{\circ}\), \(\angle AOD = 98^{\circ}\), and \(\angle AOC = 90^{\circ}\). We need to find \(\angle COD\). 2. Finding \(\angle BOD\): * We know \(\angle AOB = \angle AOD + \angle DOB\). Therefore, \(\angle DOB = \angle AOB - \angle AOD\). * Substituting the given values, we get \(\angle DOB = 123^{\circ} - 98^{\circ} = 25^{\circ}\). 3. Finding \(\angle COD\): * We know \(\angle AOC = \angle AOD - \angle COD\). Therefore, \(\angle COD = \angle AOD - \angle AOC\). * Substituting the given values, we get \(\angle COD = 98^{\circ} - 90^{\circ} = 8^{\circ}\). 4. Checking Result: * \(\angle COB = \angle AOC + \angle AOB \implies \angle COB = 90 + 123 = 213^{\circ}\). * \(\angle COD = \angle COB - \angle BOD = 213 - 25 = 188^{\circ}\). * \(\angle AOD = \angle AOC + \angle COD = 90 + \angle COD = 98 \implies \angle COD = 98 - 90 = 8^{\circ}\). Answer: 8 degrees