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WJEC MATHEMATICS
INTERMEDIATE
ANGLES AND GEOMETRY
SHAPES AND ANGLES
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Contents
Interior and Exterior Angles
Exterior angles of regular polygon
Tessellations
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Interior and Exterior Angles
 Interior angles are the angles less than 180o that are contained
within the sides of the shape
 Exterior angles are angles made outside of a shape, when a
side it extended. (Not the 180o, the other one)
 An adjacent interior and exterior angle add up to 180o
 All the exterior angles add up to 360o
An interior and
exterior angle sum to
180o
All the exterior
angles sum to
360o
Interior angles are
represented by circles
Exterior angles are
represented by
squares
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 Interior angles of a triangle sum to 180o
 Interior angles of a quadrilateral sum to 360o
These two shape facts you should know, but you can
easily calculate others
Sides
3 (Triangle)
4 (Quadrilateral)
5 (Pentagon)
6 (Hexagon)
7 (Heptagon)
8 (Octagon)
Sum of interior
angles
180
360
540
720
900
1080
Add 180
degrees
each time
Knowing the above table will save you time in an exam!
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Shape Facts Sheet
Angles in a triangle add to 180o
a + b + c = 180
Angles in a quadrilateral add to
360o
a + b + c + d = 360
Angles in an EQUILATERAL
triangle are the same
(All 60o)
The angles opposite the equal
sides in an ISOSCELES triangle
are the same
a=b
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Exam Questions G32
1.
2.
6
3.
4.
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Tessellations
Two shapes tessellate if they fit together (like tiles) with no gap in
between them.
The way to check if shapes tessellate it to either draw them to scale
(the hard way) or you can check if you can place the angles together
and get 360o.
Example
You can see these
shapes tessellate as
their interior angles
make 360o when placed
together.
Here's how we check numerically
Example 1
State whether or not a regular hexagon tessellates.
The sum of the interior angles of a regular hexagon =
So each angle
So, one angle is 120o, two angles would be 240o, three would be 360o
As we were able to make 360o a regular hexagon tessellates
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Example 2
State whether or not a regular octagon tessellates.
The sum of the interior angles of a regular octagon =
So each angle
So, one angle is 135o, two angles would be 270o, three would be
405o.
As we were unable to make 360o, regular octagons do not tessellate
Exam Questions G33
1.
2.
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3.
4.
5.
Does a regular pentagon tessellate? Nonagon?
Decagon? Dodecagon?
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