Shape and Space 1
4 marks · HardA regular polygon has an interior angle that is 165°. Calculate:
The number of sides of the polygon.
The sum of the interior angles of the polygon.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 24 · must show Uses (n-2)*180/n=165, n=24
(b) 3960° · must show (n-2)*180=3960
Common mistakes: Using wrong formula or failing to round to nearest integer (number of sides must be whole).
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Writes correct equation relating n to interior angle ( (n-2)×180/n = 165 )
M2 (a) · 1 mark · Rearranges and solves for n
A1 (a) · 1 mark · Obtains n = 24
B1 (b) · 1 mark · Correctly calculates sum = (24-2)×180 = 3960° (follow-through)
Worked solution
a) Let the number of sides be n:
(n-2)×180 = 165n
180n - 360 = 165n
15n = 360 → n = 24
b) Sum = (n-2)×180 = (24-2)×180 = 3960°