Classifying Triangles by Angles
Triangles can also be classified based on the size of their angles. In Class 4, you learn three types: acute, right, and obtuse triangles. Each type is identified by looking at the largest angle in the triangle.
This classification is useful in construction, architecture, and solving geometry problems. Every triangle has three angles that always add up to 180°.
What is Classifying Triangles by Angles - Class 4 Maths (Geometry)?
Based on angles, triangles are classified as:
| Type | Largest Angle | Property |
|---|---|---|
| Acute triangle | Less than 90° | All 3 angles are acute (less than 90°) |
| Right triangle | Exactly 90° | One angle is exactly 90° |
| Obtuse triangle | Greater than 90° | One angle is obtuse (greater than 90°) |
Sum of all angles in a triangle = 180°
Solved Examples
Example 1: Example 1: Identifying an Acute Triangle
Problem: A triangle has angles 60°, 70°, and 50°. Classify it.
Solution:
All three angles are less than 90°.
Check: 60° + 70° + 50° = 180° ✓
Answer: It is an acute triangle.
Example 2: Example 2: Identifying a Right Triangle
Problem: A triangle has angles 90°, 45°, and 45°. Classify it.
Solution:
One angle is exactly 90°.
Check: 90° + 45° + 45° = 180° ✓
Answer: It is a right triangle.
Example 3: Example 3: Identifying an Obtuse Triangle
Problem: A triangle has angles 120°, 35°, and 25°. Classify it.
Solution:
One angle (120°) is greater than 90°.
Check: 120° + 35° + 25° = 180° ✓
Answer: It is an obtuse triangle.
Example 4: Example 4: Finding the Missing Angle
Problem: A triangle has angles 55° and 90°. Find the third angle and classify the triangle.
Solution:
Step 1: Third angle = 180° − 55° − 90° = 35°
Step 2: One angle is 90° → right triangle.
Answer: Third angle = 35°; it is a right triangle.
Example 5: Example 5: Can a Triangle Have Two Right Angles?
Problem: Can a triangle have two 90° angles?
Solution:
If two angles are 90°, their sum = 180°. The third angle would be 180° − 180° = 0°.
An angle of 0° is not possible in a triangle.
Answer: No, a triangle cannot have two right angles.
Example 6: Example 6: Can a Triangle Have Two Obtuse Angles?
Problem: Can a triangle have two obtuse angles?
Solution:
If two angles are each more than 90°, their sum is already more than 180°. This violates the angle sum property.
Answer: No, a triangle can have at most one obtuse angle.
Example 7: Example 7: Equilateral Triangle Classification by Angles
Problem: An equilateral triangle has all angles equal to 60°. Is it acute, right, or obtuse?
Solution:
60° < 90°, so all angles are acute.
Answer: An equilateral triangle is always an acute triangle.
Example 8: Example 8: Word Problem
Problem: Priya drew a triangle with a 90° corner for a school project. Two of its sides are 3 cm and 4 cm. What type of triangle (by angles) did she draw?
Solution:
Since the triangle has a 90° angle, it is a right triangle.
Answer: Priya drew a right triangle.
Example 9: Example 9: Classifying with Two Given Angles
Problem: Two angles of a triangle are 40° and 30°. Classify the triangle.
Solution:
Step 1: Third angle = 180° − 40° − 30° = 110°
Step 2: 110° > 90° → obtuse.
Answer: It is an obtuse triangle.
Example 10: Example 10: Combined Classification
Problem: A triangle has sides 5 cm, 5 cm, 5 cm and all angles are 60°. Classify by sides and angles.
Solution:
By sides: all equal → equilateral.
By angles: all 60° (acute) → acute triangle.
Answer: It is an equilateral acute triangle.
Key Points to Remember
- Acute triangle: All angles less than 90°.
- Right triangle: One angle is exactly 90°.
- Obtuse triangle: One angle is greater than 90°.
- The sum of angles in any triangle = 180°.
- A triangle can have at most one right or obtuse angle.
- An equilateral triangle is always acute (all angles = 60°).
- A triangle can be classified by both sides and angles (e.g., isosceles right triangle).
Practice Problems
- A triangle has angles 70°, 60°, and 50°. Classify by angles.
- Find the missing angle: 90°, 38°, _____. Classify the triangle.
- A triangle has angles 100°, 40°, and 40°. What type is it?
- Can a triangle have angles 80°, 60°, and 50°? Why or why not?
- An equilateral triangle has what type of angles?
- Dev drew a triangle with one angle of 90° and two equal sides. Classify by sides and angles.
- True or False: A right triangle can also be isosceles.
Frequently Asked Questions
Q1. What is an acute triangle?
An acute triangle is one in which all three angles are less than 90°. Examples of angle sets: 60°-60°-60°, 50°-60°-70°.
Q2. What is a right triangle?
A right triangle has one angle that measures exactly 90°. The side opposite the right angle is the longest side, called the hypotenuse.
Q3. What is an obtuse triangle?
An obtuse triangle has one angle greater than 90°. The other two angles are acute and together add up to less than 90°.
Q4. Can a triangle have more than one obtuse angle?
No. Two obtuse angles would add up to more than 180°, which violates the angle sum property. A triangle has at most one obtuse angle.
Q5. What is the angle sum property of a triangle?
The sum of all three interior angles of any triangle is always 180°. This property is used to find missing angles.
Q6. Can a right triangle be equilateral?
No. An equilateral triangle has all angles equal to 60°. A right triangle has one 90° angle. These conditions cannot be satisfied simultaneously.
Q7. Can a right triangle be isosceles?
Yes. A right isosceles triangle has angles 90°, 45°, and 45°. The two sides forming the right angle are equal.
Q8. Is classifying triangles by angles part of NCERT Class 4?
Yes, classification of triangles by angles is part of the CBSE/NCERT Class 4 Maths curriculum under the Geometry chapter.
