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Many Class 6 students can draw a neat angle but still read the wrong number off a protractor, or decide that an angle with long arms must be bigger. Both slips come from the same gap: not yet seeing an angle as a turn. This post walks through Chapter 2 of the new NCERT book, shows how to name and measure every figure in it, works through examples with numbers, and ends with a short practice routine.
What does the Class 6 Lines and Angles chapter cover?
NCERT's Class 6 mathematics textbook is Ganita Prakash, first published in August 2024; the current copy is marked "Reprint 2026-27". Chapter 2, Lines and Angles, moves through these ideas in order:
A point marks a location and is named with a capital letter.
A line segment is the shortest path between two points, such as ST.
A line is a segment extended forever in both directions.
A ray starts at one point and goes on forever in one direction.
An angle is two rays with a common starting point, called the vertex.
The chapter then compares angles, makes "rotating arms" from two paper straws and a clip, measures angles in degrees and sorts them into types. Ask your teacher which book your school uses, since some schools move to new editions at different speeds.
How do you name a ray or an angle correctly?
Order matters for a ray but not for a segment. A ray named DP starts at D and passes through P. Writing PD describes a different ray that starts at P.
For angles, the vertex always sits in the middle of the name. The chapter's summary uses rays OP and OM, which form the angle named ∠POM or ∠MOP. Here O is the vertex, and OP and OM are the arms. Writing ∠OPM would name a different angle, with its vertex at P.
A quick check: say the name aloud and trace it with your finger. You should start on one arm, pass through the corner, and finish on the other arm.
Why is an angle about turning, not arm length?
The book defines the size of an angle as the amount of rotation needed about the vertex to turn one arm onto the other. The length of the arms plays no part. You can extend both arms of a 30° angle to the edge of the page and it stays 30°.
This is harder than it sounds. Gibson, Congdon and Levine (2015) note that when judging the size of angles, children often rely on the wrong feature, such as the length of the sides. In their study of preschoolers, children who were given a separate word for the whole figure improved more after training than children taught only the meaning of "angle". The lesson for older students is simple: keep your attention on the opening between the arms.
Why are there 360 degrees in a full turn?
The chapter divides a full turn into 360 equal parts and calls each part 1 degree. A straight angle is half a turn, so it is 180°, and a right angle is half of that, 90°.
In its "pinch of history", the chapter explains that the reason for 360 is not fully known, but notes ancient calendars of about 360 days and Babylonian counting in 60s. It adds a practical reason: 360 is the smallest number that can be divided evenly by every number from 1 to 10 except 7. You can check this yourself: 360 ÷ 8 = 45 and 360 ÷ 9 = 40, while 360 ÷ 7 leaves a remainder.
Worked example 1 (clock angles). A clock face is a full turn of 360° split into 12 hour marks, so each gap is 360 ÷ 12 = 30°. At 3 o'clock the hands are 3 gaps apart: 3 × 30 = 90°, a right angle. At 4 o'clock they are 4 × 30 = 120°, an obtuse angle.
How do you measure an angle with a protractor?
A protractor has two scales, one increasing from right to left and one from left to right. Follow these steps:
Put the centre of the protractor exactly on the vertex.
Line up the base line with one arm.
Find the scale that reads 0 on that arm.
Read where the other arm crosses that same scale.
Worked example 2. Arm BA lies along the base line on the right, where the inner scale reads 0. Arm BC crosses the inner scale at 65. So ∠ABC = 65°, an acute angle. The outer scale at the same spot reads 180 − 65 = 115, which is the wrong reading. A quick check catches it: the angle looks smaller than a right angle, so the answer must be less than 90°.
Worked example 3 (reflex angle). You measure the smaller angle between two rays as 140°. The reflex angle on the other side is 360 − 140 = 220°.
The chapter's types, by size:
Acute: more than 0° and less than 90°
Right: exactly 90°
Obtuse: more than 90° and less than 180°
Straight: exactly 180°
Reflex: more than 180° and less than 360°
Which mistakes cost the most marks?
Reading the wrong scale. Always start from the 0 that sits on an arm.
Vertex not on the centre point. Even a small shift changes the reading.
Naming with the vertex at the end. ∠ABC has vertex B.
Judging by arm length. Longer arms do not make a bigger angle.
Calling 90° acute. Acute is less than 90°; 90° is right.
How should you practise this week?
Day 1: Draw five rays from one point and name every angle you can see.
Day 2: Measure ten angles in your textbook, estimating each one first.
Day 3: Find the angle between clock hands at 1, 2, 5 and 6 o'clock.
Day 4: Draw angles of 35°, 90°, 145° and 250° with a protractor.
Day 5: Swap drawings with a friend and measure each other's angles.
If you learn better by seeing ideas move, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. Angles come back in our posts on symmetry in Class 6 and parallel and intersecting lines in Class 7.
Tonight, look at a clock, estimate the angle between its hands, and check your guess with a protractor.
