Lines, Angles and Polygons: SSC CGL Quantitative Aptitude

Formulas (3)

• Angles at crossing lines and at parallel lines · Angles at lines
  $$\text{linear pair} = 180^\circ \qquad \text{round a point} = 360^\circ \qquad \text{co-interior pair} = 180^\circ$$
• Interior and exterior angle sums of a polygon · Polygon angle sums
  $$\text{interior sum} = (n - 2) \times 180^\circ \qquad \text{exterior sum} = 360^\circ \qquad \text{interior} + \text{exterior} = 180^\circ$$
• Number of diagonals of a polygon · Diagonals of an n-sided polygon
  $$\text{diagonals} = \frac{n(n - 3)}{2}$$

Watch out for (7)

• Calling alternate angles supplementary
  → Angles at crossing lines and at parallel lines
• Using the parallel-line rules on lines that are not parallel
  → Angles at crossing lines and at parallel lines
• Using n × 180° for the interior sum
  → Interior and exterior angle sums of a polygon
• Thinking the exterior sum grows with the sides
  → Interior and exterior angle sums of a polygon
• Giving the interior angle when the exterior one is asked
  → Interior and exterior angle sums of a polygon
• Counting every pair of corners as a diagonal
  → Number of diagonals of a polygon
• Forgetting to halve
  → Number of diagonals of a polygon

Formulas (3)

• Each interior and exterior angle of a regular polygon · One angle of a regular polygon
  $$\text{exterior} = \frac{360^\circ}{n} \qquad \text{interior} = 180^\circ - \frac{360^\circ}{n} = \frac{(n - 2) \times 180^\circ}{n}$$
• Number of sides of a regular polygon from one angle · Sides from an angle
  $$n = \frac{360^\circ}{\text{exterior}} \qquad \text{exterior} = \frac{180^\circ - d}{2} \qquad n = 2(k + 1)$$
• Centre, side and area of a regular polygon · Centre angle and hexagon area
  $$\text{angle at centre} = \frac{360^\circ}{n} \qquad \text{hexagon area} = 6 \times \frac{\sqrt{3}}{4}a^2 = \frac{3\sqrt{3}}{2}a^2$$

Watch out for (7)

• Taking 360°/n as the interior angle
  → Each interior and exterior angle of a regular polygon
• Using these formulas on a polygon that is not regular
  → Each interior and exterior angle of a regular polygon
• Dividing 360 by the interior angle
  → Number of sides of a regular polygon from one angle
• Forgetting to halve when the difference is given
  → Number of sides of a regular polygon from one angle
• Accepting a polygon that cannot exist
  → Number of sides of a regular polygon from one angle
• Giving the interior angle for the angle at the centre
  → Centre, side and area of a regular polygon
• Treating the hexagon's centre distance as different from its side
  → Centre, side and area of a regular polygon