If the sum of two angles is an obtuse angle, then which of the following is not possible?

1. one right angle and one acute angle

2. one obtuse angle and one acute angle

3. two acute angles

4. two right angles

An obtuse angle is between 90° and 180°.

1. Right angle (90°) + acute angle (e.g., 20°) = 110° (obtuse) — possible.

2. Obtuse angle (e.g., 100°) + acute angle (e.g., 20°) = 120° (obtuse) — possible.

3. Two acute angles (e.g., 60° + 60°) = 120° (obtuse) — possible.

4. Two right angles = 90° + 90° = 180° (straight angle, not obtuse) — not possible.

Hence, option 4 is the correct option.