NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions

Question 53

Step 1: Know the names.

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

Step 2: Draw a base ray for all angles.

Draw a straight line starting at a point O. Mark an arrow to show it is a ray.

Step 3: Draw two acute angles without a protractor.

1. First acute (about \(35^\circ\)). Keep the opening clearly smaller than a right angle. Use a paper corner as a guide for \(90^\circ\). Take about one third of that corner. This is near \(30^\circ\)–\(35^\circ\).
2. Second acute (about \(60^\circ\)). Make the opening a little less than two thirds of a right angle. Two thirds of \(90^\circ\) is about \(60^\circ\).

Step 4: Draw one obtuse angle without a protractor.

Open the second ray wider than a right angle. Think: right angle \(= 90^\circ\), then add about \(30^\circ\). This gives about \(120^\circ\).

Step 5: Write your estimates.

• Acute 1: about \(35^\circ\).
• Acute 2: about \(60^\circ\).
• Obtuse: about \(120^\circ\).

Step 6: Check with a protractor.

1. Place the protractor’s center on the vertex O.
2. Align the baseline with the base ray.
3. Read the scale that starts from \(0^\circ\) on your base ray.
4. Note the measured value for each angle.

Step 7: Compare.

Write the actual readings and see how close they are to your estimates. Example: \(34^\circ\), \(62^\circ\), \(119^\circ\).