Triangles and angles Types
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Angle Types and Triangle Classification
1️⃣ Understand three types of angles based on measurements
2️⃣ Learn to classify triangles by their angles
3️⃣ Master the triangle angle sum property
4️⃣ Apply angle rules to identify triangle types
5️⃣ Remember why triangle naming conventions differ
1️⃣ Three Types of Angles
Angles are classified into three main types based on their measurements. Understanding these classifications is fundamental to geometry and triangle analysis.
Three Types of Angles
Acute Angle
Less than 90°
Sharp angle, like the corner of a slice of pizza
Right Angle
Exactly 90°
Perfect corner, like the corner of a book
Obtuse Angle
Greater than 90°
Wide angle, like an open book
Key Memory Aid: Think of angle types like opening a door - acute is barely open, right is halfway, obtuse is wide open!
2️⃣ Triangle Classification by Angles
Based on the types of angles they contain, triangles are classified into three main categories. Each type has unique properties and characteristics.
Triangle Angle Sum Property
The sum of all interior angles in any triangle = 180°
This is true for ALL triangles, regardless of their shape or size!
Three Types of Triangles by Angles
Acute Triangle
ALL angles 
All three angles are acute (less than 90°). This triangle appears "sharp" with no wide angles.
Example: 60°, 70°, 50°
Right Triangle
ONE angle 
Exactly one angle is a right angle (90°). The other two angles are acute and complementary.
Example: 90°, 30°, 60°
Obtuse Triangle
ONE angle 
Exactly one angle is obtuse (greater than 90°). The other two angles are acute.
Example: 120°, 30°, 30°
Important Rule: In any triangle, there can be AT MOST one right angle or one obtuse angle. Why? Because if there were two, their sum would exceed 180°!
3️⃣ Understanding the Triangle Names
Notice the naming pattern: we say "acute triangles" (plural) but "right triangle" and "obtuse triangle" (singular). This reflects mathematical constraints!
Why Different Names?
Right Triangle (Singular)
A triangle can have AT MOST one right angle. If it had two 90° angles, that would be 180° total, leaving no room for a third angle!
Obtuse Triangle (Singular)
A triangle can have AT MOST one obtuse angle. Two obtuse angles would exceed 180°, which is impossible in a triangle.
Acute Triangles (Plural)
ALL THREE angles can be acute! For example: 80°, 60°, and are all less than 90° and sum to 180°. That's why we use the plural form.
4️⃣ Practical Examples
Test Your Understanding
Example 1: Classify the Triangle
A triangle has angles measuring 75°, 60°, and 45°. What type of triangle is this?
Solution:
Check: 
✓
All angles are less than 90° (all acute)
Answer: Acute Triangle
All angles are less than 90° (all acute)
Answer: Acute Triangle
Example 2: Find the Missing Angle
In a triangle, two angles measure 35° and 90°. Find the third angle and classify the triangle.
Solution:
Use angle sum: 
Third angle =
One angle = 90°
Answer: Right Triangle with third angle = 55°
Third angle =
One angle = 90°
Answer: Right Triangle with third angle = 55°
Key Points to Remember
🔸 Acute: | Right:
| Obtuse:
🔸 All triangle angles sum to 180°
🔸 Acute Triangle: ALL angles acute
🔸 Right Triangle: ONE right angle exactly
🔸 Obtuse Triangle: ONE obtuse angle only