The diagram shows a hexagon - Edexcel - GCSE Maths - Question 6 - 2019 - Paper 3
Question 6
The diagram shows a hexagon.
The hexagon has one line of symmetry.
$AF = BC$
$EF = CD$
Angle $ABC = 117^{ ext{o}}$
Angle $BCD = 2 \times angle \; CDE$
Work out th... show full transcript
Worked Solution & Example Answer:The diagram shows a hexagon - Edexcel - GCSE Maths - Question 6 - 2019 - Paper 3
Step 1
Find the sum of the interior angles of a hexagon
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Answer
The formula for the sum of the interior angles of a polygon with ( n ) sides is given by:
Sum=(n−2)×180∘
For a hexagon, where ( n = 6 ):
Sum=(6−2)×180∘=4×180∘=720∘
Step 2
Determine the angles in the hexagon
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Answer
Since the hexagon has one line of symmetry, the opposite angles are equal. Let:
Angle ( AFE = x )
Then angle ( BCD = 2 \times angle , CDE )
The interior angles of the hexagon become:
x+117∘+2y+y+y+y=720∘
Where ( y ) is the angle ( CDE ).
This simplifies to:
x+117∘+5y=720∘(1)
Step 3
Establish the relationships between the angles
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Answer
From the properties of angles:
Since angle ( BCD = 2y ):
So,
BCD+CDE=3y=117∘→y=39∘.
Substituting ( y ) in (1):
x+117∘+5(39∘)=720∘
This gives:
x+117∘+195∘=720∘
Step 4
Calculate the value of angle AFE
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Answer
Thus,
x+312∘=720∘
Now, isolating ( x ):
x=720∘−312∘=408∘.
To find the angle ( AFE ):
AFE=408∘−360∘=48∘.
