What this chapter is about
This chapter introduces you to the world of lines and angles. You will learn what a point, a line and a line segment are. You will also learn about rays and how they are different from lines.
The second big idea is angles. An angle is formed when two rays meet at a common point. You will learn how to name angles, compare them and measure them using a tool called a protractor. You will meet different types of angles based on their size.
After studying this chapter, you should be able to draw lines and angles, measure angles in degrees, and tell the difference between types of angles like right angles, acute angles and obtuse angles.
Key ideas
- A point is a dot that shows an exact position. It has no length, width or height.
- A line goes on forever in both directions. We show it with arrows on both ends.
- A line segment is a part of a line with two endpoints. It has a fixed length.
- A ray starts at one point and goes on forever in one direction. The sun's rays are a good example.
- An angle is formed when two rays share the same starting point. That shared point is called the vertex.
- Angles are measured in degrees. The symbol for degrees is °.
- A right angle measures exactly 90°. The corner of a book or a door makes a right angle.
- An acute angle is smaller than a right angle, meaning it is less than 90°.
- An obtuse angle is larger than a right angle but smaller than a straight line, meaning it is between 90° and 180°.
Formulas and facts to remember
- Right angle = 90° (the angle at the corner of a square)
- Straight angle = 180° (the angle on a straight line)
- Complete angle = 360° (one full turn, like a clock hand going all the way around)
- Acute angle: any angle more than 0° but less than 90°
- Obtuse angle: any angle more than 90° but less than 180°
- Two rays forming an angle share a common point called the vertex.
Worked examples
Example 1: Naming an angle
Two rays start from point B. One ray goes towards A and the other towards C. What is the name of the angle?
Solution: The vertex is B because both rays start there. The angle is named using three letters: A-B-C with the vertex in the middle. So the angle is called angle ABC or angle CBA.
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Example 2: Measuring and identifying an angle
Riya measured an angle with her protractor and got 55°. What type of angle is this?
Solution: A right angle is 90°. Since 55° is less than 90°, this angle is smaller than a right angle. So it is an acute angle.
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Example 3: Finding a missing angle
Amit turned around completely on the playground. He first turned 150° and then turned some more to complete a full turn. How many more degrees did he turn?
Solution: A complete turn is 360°. He already turned 150°. Remaining turn = 360° − 150° = 210°. So Amit turned 210° more to complete his full turn.
Common mistakes
- Drawing a line segment with arrows on both ends → A line segment has dots at both ends (endpoints), not arrows.
- Thinking that a bigger-looking angle is always more degrees → Always measure with a protractor; the length of the arms does not decide the angle.
- Reading the wrong scale on a protractor → Check whether your angle opens from 0° on the inner scale or the outer scale.
- Confusing rays and line segments → A ray has one endpoint and goes on forever in one direction, while a line segment has two endpoints.
- Forgetting to put the vertex at the centre of the protractor → The vertex must sit exactly at the centre mark when measuring.
Quick revision
- A point shows position. A line has no end. A line segment has two ends. A ray has one end.
- Angle = two rays sharing one vertex.
- Right angle = 90°, Acute angle < 90°, Obtuse angle > 90° but < 180°.
- A full turn = 360°, a straight line = 180°.
- Use a protractor to measure angles in degrees.