NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Multiple Choice Questions

Question 12

Key facts

• Acute angle: \(0^circ < \theta < 90^circ\).
• Right angle: \(\theta = 90^\circ\).
• Obtuse angle: \(90^\circ < \theta < 180^\circ\).
• Straight angle: \(\theta = 180^\circ\).

Check each option

1. One obtuse + one acute

   Choose examples: \(100^\circ\) (obtuse) and \(20^\circ\) (acute).

   Sum: \(100^\circ + 20^\circ = 120^\circ\).

   \(120^\circ\) is obtuse. So this is possible.

2. One right + one acute

   Right angle: \(90^\circ\). Let acute be \(\alpha\) with \(0^\circ < \alpha < 90^\circ\).

   Sum: \(90^\circ + \alpha\).

   Since \(0^\circ < \alpha < 90^\circ\), we get \(90^\circ < 90^\circ + \alpha < 180^\circ\).

   The sum is obtuse. So this is possible.

3. Two acute angles

   Let the angles be \(\alpha\) and \(\beta\) with \(0^\circ < \alpha,\beta < 90^\circ\).

   Pick \(\alpha = 50^\circ\), \(\beta = 50^\circ\).

   Sum: \(50^\circ + 50^\circ = 100^\circ\).

   \(100^\circ\) is obtuse. So this is possible.

4. Two right angles

   Sum: \(90^\circ + 90^\circ = 180^\circ\).

   \(180^\circ\) is a straight angle, not obtuse.

   So this is not possible if the sum must be obtuse.

Answer: Option D — Two right angles.