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Grade 6/ Mathematics/ Lines and Angles
Chapter 2 · NCERT Class 6 Ganita Prakash

Lines and Angles

Start with a single dot, stretch it into a line, then let two lines meet and an angle is born. From the corner of a book to the hands of a clock, angles are everywhere – and a protractor lets you measure them exactly. Tap each idea to draw it in your head.

📐 3 topics⏱ ~25 min📝 12-question quiz
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Six building blocks of geometry

Geometry begins with a point and grows from there. Tap each term to see what it means and how it connects to angles.

Explore · Lines & Anglestap a term

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The three big ideas

  • Point – an exact position with no length, width or thickness. We draw a dot and name it with a capital letter, like P.
  • Line segment – the straight path between two endpoints; it has a definite length. Segment AB joins A to B.
  • Ray – starts at one endpoint and goes on forever in one direction (like a torch beam).
  • Line – extends endlessly in both directions; it has no endpoints. We mark arrows on both ends.
Common mistake: calling every straight mark a "line". If it has two ends it is a segment; one end and an arrow makes a ray; arrows on both ends make a line.
  • An angle is formed by two rays (its arms) starting from a common point, the vertex. The amount of turn between the arms is measured in degrees (°).
  • Acute – less than 90°.   Right – exactly 90°.   Obtuse – between 90° and 180°.
  • Straight – exactly 180° (the arms make a straight line).   Reflex – between 180° and 360°.   A full turn is 360°.
  • A bigger angle means a bigger turn, not longer arms – the length of the arms does not change the angle.

Worked example. What angle do a clock's hands make at 3 o'clock, and what type is it?

Step 1. A full clock face is one complete turn = 360°.

Step 2. The 12 hour-marks divide it equally: 360° ÷ 12 = 30° per mark.

Step 3. From 12 to 3 is 3 marks: 3 × 30° = 90° – a right angle.

  • A protractor is a half-circle marked from 0° to 180° with two scales running opposite ways.
  • To measure: place the protractor's centre on the vertex, line one arm along the 0° line, then read where the second arm crosses the scale.
  • Use the scale that starts from the arm sitting on 0° – this avoids reading the wrong number.
  • To draw an angle (say 60°): draw one arm, mark 60° from the 0° line, then join the vertex to that mark.
Common mistake: reading the wrong scale. If your arm sits on 0° on the inner scale, read the inner scale – otherwise a 60° angle is misread as 120°. The two always add up to 180°.

Where you'll meet it

Angles at work

Carpentry & building

A carpenter checks corners with a set-square to make sure they are right angles (90°). Walls, doors and tiles only fit neatly when their angles are exact – a small error grows into a big gap across a room.

Ramps & cricket

A wheelchair ramp uses a small (acute) angle so it is easy to climb; a batter judges the angle of the bat to send the ball where they want. The size of the angle decides the result.

Clocks & directions

Clock hands sweep through angles all day, and a compass splits directions into 360°. Knowing that a quarter-turn is 90° helps you describe turns precisely – "turn 90° to your right".

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

Score 0/12

Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 6 Ganita Prakash textbook (ncert.nic.in).

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