Chapter 6 · NCERT Class 9 Maths

Lines and Angles

Two lines, a few angles, and a handful of rules that never break. Once you know which pairs add to 90°, which add to 180°, and which are simply equal, geometry stops being guesswork. Tap each pair to see exactly how it behaves.

📐 3 topics⏱ ~22 min📝 12-question quiz

Play with it

The pairs of angles

Every angle relationship in this chapter is one of these six. Tap each to see what it means and the single rule it obeys — sum to 90°, sum to 180°, or simply equal.

Explore · Angle pairstap a pair

Learn

The three big ideas

Complementary angles — two angles whose measures add up to 90°.
Supplementary angles — two angles whose measures add up to 180°.
Adjacent angles — share a common vertex and a common arm, with no overlap.
Linear pair — two adjacent angles whose non-common arms form a straight line; they always add up to 180°.

Worked example. Angles A and B are complementary and A = 50°. Find B. Also, a line has a linear pair where one angle is 110° — find the other.

Complementary → A + B = 90°, so B = 90° − 50° = 40°.

Linear pair → the two angles sum to 180°, so the partner = 180° − 110° = 70°.

Common mistake: swapping the two sums. Complementary angles add to 90°; supplementary angles add to 180°. Mix them up and every answer will be off by 90°.

When two straight lines cross, they make four angles at the point of intersection.
The angles directly facing each other — the vertically opposite angles — are always equal.
Any two angles side by side form a linear pair, so they add up to 180°.

A transversal is a line that cuts two other lines. When those two lines are parallel, special pairs appear.
Corresponding angles (matching corners) are equal.
Alternate interior angles (the Z-shaped pair between the lines) are equal.
Co-interior angles (same-side interior) are supplementary — they add up to 180°.

Where you'll meet it

Angles at work

Carpentry & construction

Carpenters and builders rely on these rules every day — cutting joints to complementary angles, checking that a corner is a true 90°, and using linear pairs to keep beams and walls straight.

Mirrors & reflection

Light bounces off a mirror so the angle of incidence equals the angle of reflection — the same "equal angles" idea behind vertically opposite and alternate angles. It is what makes periscopes and kaleidoscopes work.