Concept 8 of 8Foundation

📌 Formula Sheet — Lines and Angles

All the angle relationships in one place. Learn WHY each holds.

Complementary: ∠1 + ∠2 = 90°

Means: two angles that together make a right angleUse when: you know one, find the other

Why: Two angles fit inside a corner of 90°. Their measures together must equal 90°.

⚠ Trap: Complementary does NOT mean equal — only their SUM is fixed.

Supplementary: ∠1 + ∠2 = 180°

Means: two angles together form a straight angleUse when: linear pairs, co-interior angles

Why: A straight line represents 180°. Two angles along it share that total.

⚠ Trap: Don't confuse 'supplementary' (sums to 180°) with 'complementary' (sums to 90°). C < S alphabetically = 90° < 180°.

Vertically opposite angles are EQUAL

Means: two crossing lines create 4 angles; opposite pairs are equalUse when: two lines intersect

Why: If ∠a and ∠b form a linear pair, ∠a + ∠b = 180°. If ∠b and ∠c also form a linear pair, ∠b + ∠c = 180°. Subtracting: ∠a = ∠c.

⚠ Trap: 'Adjacent' angles (next to each other) are supplementary, NOT equal.

Sum of angles in a triangle = 180°

Means: ∠A + ∠B + ∠C = 180°Use when: two angles known, find third

Why: Draw a line through one vertex parallel to the opposite side. The three angles at that vertex equal the three triangle angles (using alternate angles). They sit on a straight line → 180°.

⚠ Trap: An exterior angle of a triangle equals the SUM of the two remote interior angles (not all three).

Sum of angles in an n-sided polygon = (n − 2) × 180°

Means: interior angle sum for any polygonUse when: quadrilateral (360°), pentagon (540°), hexagon (720°), etc.

Why: Any n-gon can be divided into (n − 2) triangles from one vertex. Each triangle contributes 180°.

⚠ Trap: Works only for CONVEX polygons. A regular n-gon has equal angles — divide the sum by n.

Parallel + transversal: corresponding & alternate angles EQUAL; co-interior SUPPLEMENTARY

Means: if ℓ₁ ∥ ℓ₂, the special pairs follow these rulesUse when: geometry problems with parallel lines

Why: Parallel lines maintain the same "direction" — a transversal meets both at identical angles. The 'Z' shape shows alternate angles as equal; 'C' shape shows co-interior summing to 180°.

⚠ Trap: These rules need the lines to BE parallel. Without confirmation of parallelism, they don't apply.

💡 Tip:Clock angle trick: hour hand moves 30°/hour (360°/12) and 0.5°/min. Minute hand moves 6°/min.

▶Prefer a video? Open YouTube search for “angles formula revision class 6”↗