Geometry (Classes VI–VIII) • Topic 2 of 6

Lines & Angles

Angles are the most computation-heavy part of the chapter, so the facts have to be reflexes. Two angles are complementary if they add to 90° and supplementary if they add to 180°. When two lines cross, the angles directly across from each other (vertically opposite) are equal, and a linear pair on a straight line adds to 180°. When a transversal cuts two parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior (same-side interior) angles add to 180° — CTET reliably asks one of these. Pedagogically this sits at van Hiele Level 1–2: the child moves from 'this looks like a right angle' to measuring with a protractor (a notorious source of error: reading the wrong scale, or not placing the centre on the vertex) and finally to reasoning 'these must be equal because the lines are parallel'. The classic misconception is that a bigger-looking arm means a bigger angle — children confuse the length of the rays with the amount of turn. CTET mixes pure computation ('find the supplement of 67°') with diagram reasoning and with the protractor misconception.

✅ Solved examples

1. The supplement of an angle of 115° is:
Supplementary angles add to 180°, so the supplement is 180° − 115° = 65°.
2. Two angles form a linear pair. One of them is 3 times the other. Find both angles.
A linear pair adds to 180°. Let the smaller be x; then x + 3x = 180°, so 4x = 180°, x = 45°. The angles are 45° and 135°.
3. A pupil insists an angle drawn with long arms is 'bigger' than the same opening drawn with short arms. The misconception is that angle size depends on:
The length of the rays/arms. In fact an angle measures the amount of turn (rotation) between the rays, not how long the rays are drawn. Use a transparency overlay of the two openings to show they coincide.
4. A transversal cuts two parallel lines. One co-interior (same-side interior) angle is 110°. Find the other co-interior angle.
Co-interior angles between parallel lines are supplementary, so the other is 180° − 110° = 70°.

✏️ Practice — try these, take hints as needed

1. The complement of an angle measuring 28° is:
Complementary angles add to 90°.
90 − 28.
62°
2. Two lines intersect. One of the four angles is 70°. The angle vertically opposite to it measures:
Vertically opposite angles are equal.
70°
3. When a transversal crosses two parallel lines, a pair of alternate interior angles are always:
Not supplementary.
They match.
Equal
4. An angle is equal to its own supplement. The angle is:
x + x = 180.
Half of 180.
90°

📝 Topic test — 8 questions

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