Quadrilaterals & Polygons — SSC Quant Notes Ch. 21

Introduction

Quadrilaterals & Polygons tests recognition of specific shape properties and the general polygon angle-sum formulas — a chapter of memorised facts more than heavy calculation.

Properties of Common Quadrilaterals

Shape	Key Properties
Parallelogram	Opposite sides equal & parallel; opposite angles equal; diagonals bisect each other
Rectangle	Parallelogram + all angles 90°; diagonals equal
Rhombus	Parallelogram + all sides equal; diagonals bisect at 90°
Square	Rectangle + Rhombus properties combined (all sides equal, all angles 90°, diagonals equal and perpendicular)
Trapezium	Only one pair of parallel sides (unequal in length)
Kite	Two pairs of adjacent equal sides; diagonals perpendicular

Angle Sum of a Quadrilateral

Sum of interior angles of any quadrilateral = 360°.

Q. The angles of a quadrilateral are in the ratio 2:3:4:6. Find the largest angle.

Total parts = 2+3+4+6 = 15
Largest angle = (6/15) × 360 = 144°

Regular Polygon Formulas

Flowchart — Key Polygon Angle Formulas

For a polygon with n sides

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Sum of interior angles = (n−2) × 180°

Sum of exterior angles = 360° (always, for any polygon)

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Each interior angle (regular) = [(n−2)×180°]/n

Each exterior angle (regular) = 360°/n

Q. Find each interior angle of a regular hexagon (n=6).

Interior angle = [(6−2)×180]/6 = (4×180)/6 = 720/6 = 120°

Q. If each exterior angle of a regular polygon is 24°, find the number of sides.

n = 360/24 = 15 sides

Number of Diagonals in a Polygon

Formula
Number of diagonals = n(n−3)/2

Q. Find the number of diagonals in a regular octagon (n=8).

Diagonals = 8×(8−3)/2 = 8×5/2 = 20

💡 Exam Tip: "Interior + Exterior angle at any vertex = 180°" always holds (linear pair) — a quick cross-check when solving polygon angle questions.

✅ Practice Focus: Property recall for parallelogram/rhombus/trapezium/kite · Interior angle sum formula (n−2)×180° · Exterior angle sum (always 360°) · Diagonal-count formula n(n−3)/2.

← Back to Triangles Next Chapter → Circles

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