Circles and Polygons

Quick Summary
External angle = 360/n
For a regular polygon with ‘n’ sides:
Internal angle = 180 – 360/n
Polygon:    Sides        Ex angles    In angles:
Triangle    3    120    60
Square    4    90    90
Pentagon    5    72    108
Hexagon    6    60    120
Heptagon    7    51.4    128.6
Octagon    8    45    135
Nonagon    9    40    140
Decagon    10    36    144
Undecagon    11    32.7    147.3
Dodecagon    12    30    150
Special types of triangles
Sides
Equilateral — All 3 sides equal and all 3 angles equal (to 60o).
Isosceles — Two sides the same and the angles at the bottom of those sides are equal.
Scalene — No sides or angles equal.
Angles
Acute-angled — All angles are acute (less than 90o).
Right-angled — One angle is 90o.
Obtuse-angled — One angle is obtuse (greater than 90o).
Quadrilaterals:
Square — All sides equal, all angles 90o, 4 lines of symmetry, rotation symmetry of order 4.
Rectangle — Two pairs of equal and parallel sides, all angles 90o, two lines of symmetry, rotation symmetry of order 2.
Rhombus — All sides equal, opposite sides parallel, two lines of symmetry, rotation symmetry of order 2. (Basically a square leaning over. Sometimes referred to as a diamond!
Parallelogram — Two pairs of equal and parallel sides, opposite angles equal, no lines of symmetry, rotation symmetry of order 2. (Basically a rectangle leaning over.).
Trapezium — One pair of parallel sides, no symmetry.
Kite — Two pairs of equal sides next to each other, one line of symmetry, no rotation symmetry, string (only joking!).
Circles
Circumference = 2πr
Or, if you want to use the diameter:
Circumference = πd
Area = πr2
Exam type question

Image 1
The diagram above is the net of a solid.
(i) Write down the name of the solid.
(1 mark)
(ii) Measure and write down the size of the angle marked x.
(1 mark)
(iii) Draw the lines of symmetry on the diagram.
(2 marks)
(iv) The diagram also has rotational symmetry.
Write down the order of rotational symmetry.
(1 mark)
(Marks available: 5)
Answers
(i) (Square) Pyramid.
(ii) Anything between 51° and 55° is an acceptable answer.
(iii) 4 correct lines drawn.
(iv) 4

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