Draw an obtuse angle. Then bisect this angle and measure the angles so obtained.

To solve this problem step by step:

Draw an Obtuse Angle:

An obtuse angle is an angle greater than 90° but less than 180°.
Start by drawing any angle where the angle between the two rays is larger than 90° but smaller than 180° (e.g., 120°).
Bisect the Angle:

To bisect the angle, use a compass and a straightedge.
Place the compass' point at the vertex of the angle.
Draw arcs that intersect both rays of the angle.
Without changing the compass width, place the compass' point at each of the intersection points and draw two new arcs that intersect each other.
Draw a straight line from the vertex of the angle through the point of intersection of these arcs. This is the angle bisector.
Measure the Angles:

Since the angle was obtuse, let's assume it was 120°.
The angle bisector divides the angle into two equal parts.
Therefore, each of the two new angles formed by the bisector will be 120° / 2 = 60°.
Conclusion:

After bisecting an obtuse angle (e.g., 120°), the two angles formed will each measure 60°.
This process works for any obtuse angle: after bisecting, each of the two new angles will be half of the original obtuse angle.