1. 🔑 Important Keywords and Definitions
Angle: An angle is formed when two rays originate from the same endpoint.
Vertex: The common endpoint of the two rays forming an angle.
Arms: The two rays forming an angle.
Interior of an Angle: The space between the arms of an angle.
Exterior of an Angle: The space outside the arms of an angle.
Degree (°): The unit used to measure an angle.
2. 🧠 Key Concepts and Explanations
An angle has three parts: the vertex, and two arms (rays).
Naming an Angle: Write the letters in order of arms-vertex-arms. For example, ∠ABC, where B is the vertex.
Angles are measured in degrees (°) using a protractor.
The size of an angle depends on the opening between the arms, not their length.
3. 📏 Formulas and Rules
Full angle = 360°
Straight angle = 180°
Right angle = 90°
1 complete rotation = 360°
To classify angles, check their degree:
Type of Angle Measure Acute Angle Less than 90° Right Angle Exactly 90° Obtuse Angle Between 90°–180° Straight Angle Exactly 180° Reflex Angle Between 180°–360° Complete Angle Exactly 360°
4. 🔄 Step-by-Step Methods
To Measure an Angle:
Place the midpoint of the protractor on the vertex.
Align one arm with the base line of the protractor.
Read the degree measure on the arc where the second arm falls.
To Draw an Angle:
Draw a ray using a ruler.
Place the protractor with its center on the endpoint of the ray.
Mark the required degree.
Join the marked point with the endpoint to form an angle.
5. ✅ Examples with Full Solutions
Example 1:
Measure and name the angle formed below.
→ [Diagram showing ∠ABC measured at 60°]
Solution:
It is an acute angle. ∠ABC = 60°
Example 2:
Draw an angle of 120°.
Solution:
Draw ray AB.
Place protractor on point A.
Mark 120°.
Draw ray AC through the mark.
∠CAB = 120°, which is an obtuse angle.
6. ⚠️ Common Mistakes to Avoid
Don’t forget to place the center of the protractor on the vertex.
Check whether you are reading the inner or outer scale of the protractor.
Don’t assume angle type by appearance—measure it properly.
Writing angle names incorrectly (e.g., writing ∠BAC instead of ∠ABC when B is vertex).
7. ✍️ Practice Questions
Classify the following angles: 35°, 90°, 140°, 180°, 220°, 360°
Draw angles of: 45°, 90°, 120°, 180°, 270°
Identify the arms and vertex in ∠PQR.
Measure and classify the given angles from textbook diagrams.
Write the names of any 3 objects around you that form an angle.
8. 📊 Conceptual Diagrams
Diagram showing acute, right, obtuse, straight, reflex, and complete angles.
Parts of an angle (arms, vertex, interior, exterior).
Protractor reading example.
9. 💡 Word Problems Section
Q: A clock shows 3 o’clock. What angle is formed between the hour and minute hand?
A: 90°, which is a right angle.
Q: A road turns at an angle of 120°. What type of angle is it?
A: Obtuse angle.
10. 📝 Important Points / Quick Revision
Angles are measured in degrees (°).
Use a protractor to measure angles.
90° = right angle; < 90° = acute; > 90° and < 180° = obtuse
Always write the vertex in the middle when naming an angle.
11. 🔗 Connections to Other Chapters
This chapter connects to:
Geometry (Polygons, Triangles)
Symmetry and Construction
Circles and Rotations (in later classes)
12. 🎯 Extra Tips or Tricks
When two lines intersect, the opposite (vertically opposite) angles are equal.
Always carry a sharp pencil and clean protractor for angle drawing.
Practice drawing and measuring angles daily to improve accuracy.