The diagram shows a square, a regular hexagon and part of another regular polygon meeting at point P - OCR - GCSE Maths - Question 18 - 2018 - Paper 1
Question 18
The diagram shows a square, a regular hexagon and part of another regular polygon meeting at point P.
(a) Show that the size of one interior angle of a regular hexa... show full transcript
Worked Solution & Example Answer:The diagram shows a square, a regular hexagon and part of another regular polygon meeting at point P - OCR - GCSE Maths - Question 18 - 2018 - Paper 1
Step 1
Show that the size of one interior angle of a regular hexagon is 120°.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To find the interior angle of a regular hexagon, we can use the formula for the interior angle of a regular polygon:
extInteriorAngle=n(n−2)×180
For a hexagon, the number of sides (n) is 6. Thus,
extInteriorAngle=6(6−2)×180=64×180=6720=120°
Hence, the interior angle of a regular hexagon is indeed 120°.
Step 2
Find the number of sides of the other regular polygon.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Let the number of sides of the other regular polygon be denoted by n.
From the diagram, we can deduce that the angles at point P should sum to 360°:
120°+(n−2)×180/n=360°
Simplifying this, we find:
Multiply the formula for interior angle by n:
(n−2)×180+120n=360n
Rearranging gives:
180n−360+120n=360n
Combining like terms results in:
300n−360=360n
Thus, solving for n:
360n−300n=36060n=360n=12
Therefore, the other regular polygon has 12 sides.
