Реши задачи на измерение углов

1. \(\angle AOC = 120^\circ\), \(\angle AOB = 3 \angle BOC\), \(\angle AOB\), \(\angle BOC\) - ? \(\angle AOC = \angle AOB + \angle BOC\) \(120^\circ = 3 \angle BOC + \angle BOC\) \(120^\circ = 4 \angle BOC\) \(\angle BOC = 30^\circ\) \(\angle AOB = 3 \cdot 30^\circ = 90^\circ\) 2. \(\angle AOC = 150^\circ\), \(\angle BOC = 4 \angle AOB\), \(\angle AOB\), \(\angle BOC\) - ? \(\angle AOC = \angle AOB + \angle BOC\) \(150^\circ = \angle AOB + 4 \angle AOB\) \(150^\circ = 5 \angle AOB\) \(\angle AOB = 30^\circ\) \(\angle BOC = 4 \cdot 30^\circ = 120^\circ\) 3. \(\angle AOB = 125^\circ\), \(\angle AOD = 20^\circ\), \(\angle COB = 25^\circ\), \(\angle COD\) - ? \(\angle AOB = \angle AOD + \angle DOC + \angle COB\) \(125^\circ = 20^\circ + \angle DOC + 25^\circ\) \(\angle COD = 125^\circ - 20^\circ - 25^\circ = 80^\circ\) 4. \(\angle AOB = 130^\circ\), \(\angle AOD = 20^\circ\), \(\angle COD = 45^\circ\), \(\angle COB\) - ? \(\angle AOB = \angle AOD + \angle DOC + \angle COB\) \(130^\circ = 20^\circ + 45^\circ + \angle COB\) \(\angle COB = 130^\circ - 20^\circ - 45^\circ = 65^\circ\) 5. \(\angle AOC = 120^\circ\), OD - биссектриса \(\angle AOC\), \(\angle AOB = 3 \angle BOC\), \(\angle AOB\), \(\angle BOC\) - ? \(\angle AOC = \angle AOB + \angle BOC\) \(120^\circ = 3 \angle BOC + \angle BOC\) \(120^\circ = 4 \angle BOC\) \(\angle BOC = 30^\circ\) \(\angle AOB = 3 \cdot 30^\circ = 90^\circ\) \(\angle AOD = \angle COD = \frac{1}{2} \angle AOC = 60^\circ\) 6. \(\angle AOC = 150^\circ\), \(\angle COD = 4 \angle AOD\), OB - биссектриса \(\angle AOC\), \(\angle BOD\) - ? \(\angle AOC = \angle AOD + \angle COD\) \(150^\circ = \angle AOD + 4 \angle AOD\) \(150^\circ = 5 \angle AOD\) \(\angle AOD = 30^\circ\) \(\angle COD = 4 \cdot 30^\circ = 120^\circ\) \(\angle AOB = \angle BOC = \frac{1}{2} \angle AOC = 75^\circ\) \(\angle BOD = \angle BOC + \angle COD = 75^\circ + 120^\circ = 195^\circ\) 7. \(\angle BOC = 80^\circ\), \(\angle AOB = 3 \angle AOC\), \(\angle AOC\), \(\angle AOB\) - ? \(\angle AOB = \angle AOC + \angle BOC\) \(3 \angle AOC = \angle AOC + 80^\circ\) \(2 \angle AOC = 80^\circ\) \(\angle AOC = 40^\circ\) \(\angle AOB = 3 \cdot 40^\circ = 120^\circ\) 8. \(\angle BOC = 60^\circ\), \(\angle AOB = 4 \angle AOC\), \(\angle AOB\), \(\angle AOC\) - ? \(\angle AOB = \angle AOC + \angle BOC\) \(4 \angle AOC = \angle AOC + 60^\circ\) \(3 \angle AOC = 60^\circ\) \(\angle AOC = 20^\circ\) \(\angle AOB = 4 \cdot 20^\circ = 80^\circ\)