1. The problem is to construct an angle \(\angle AOB\) such that \(\angle AOB = 45^\circ\). 2. To create a 45-degree angle, we use the fact that 45 degrees is half of 90 degrees, which is a right angle. 3. Start by drawing a straight line segment \(OB\). 4. At point \(O\), construct a perpendicular line to \(OB\) to form a 90-degree angle. 5. Bisect the 90-degree angle to get two 45-degree angles. 6. The bisector line from \(O\) will create \(\angle AOB = 45^\circ\). 7. This method uses the angle bisector theorem and basic geometric construction rules. Thus, \(\angle AOB = 45^\circ\) is constructed by bisecting a right angle at point \(O\).