Grade 6 Lines and Angles - Classifying angles

 

Introductory Question

Question: Angles are classified into three groups as shown below. Right angles are shown in the second group. What could be the common feature of the other two groups?

• Answer:
  • First Group (Left): All angles are less than a right angle ($< 90^\circ$). These are called acute angles.
  • Third Group (Right): All angles are greater than a right angle but less than a straight angle ($90^\circ < \text{angle} < 180^\circ$). These are called obtuse angles.

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Figure It Out

Question 1

Identify acute, right, obtuse and straight angles in the previous figures.

• Answer:
  • First group: Acute angles (e.g., \(30^\circ,45^\circ,60^\circ)\).
  • Second group: Right angles (exactly \(90^\circ)\).
  • Third group: Obtuse angles (e.g., \(120^\circ, 135^\circ)\).

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Question 2

Make a few acute angles and a few obtuse angles. Draw them in different orientations.

• Answer:

Question 3
Do you know what the words acute and obtuse mean? Acute means sharp and obtuse means blunt. Why do you think these words have been chosen?

Answer:
The word "acute" is derived from Latin words meaning sharp or pointed. Visually, the vertex of an acute angle forms a sharp, narrow tip.
The word "obtuse" means dull or blunt. Visually, an obtuse angle opens up wide, making the tip look blunt rather than sharp.

Question 4
Find out the number of acute angles in each of the figures below. What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers?

Answer:
Figure 1: 3 acute angles.
Figure 2: 12 acute angles.
Figure 3: 21 acute angles.

Pattern: 

Each step adds an inverted triangle inside the central region, which introduces exactly 9 new acute angles to the shape.

\(\text{Pattern: } 3 \rightarrow (+9) \rightarrow 12 \rightarrow (+9) \rightarrow 21\)
Next Figure Prediction: 

The next figure will continue this innermost subdivision step, and it will have:
\(\text{Total Acute Angles} = 21 + 9 = \mathbf{30}\)