Class 9 · Chapter 6

Lines and Angles

Complementary and supplementary angles, vertically opposite angles, properties of parallel lines cut by a transversal, angle sum of a triangle.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

Two angles are complementary if their sum is

90^\circ

; supplementary if

180^\circ

. Angles at a point sum to

360^\circ

. Angles on a straight line sum to

180^\circ

. Vertically opposite angles (formed by two intersecting lines) are always equal.

Key concepts & formulas

Angles on a straight line sum to

180^\circ

Vertically opposite angles are equal.

Alternate interior angles on parallel lines are equal.

Co-interior (allied) angles on parallel lines sum to

180^\circ

Angle sum of a triangle

= 180^\circ

Exterior angle of a triangle

=

sum of two opposite interior angles.