Polygon angles
AQA GCSE Maths revision on Polygon angles. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
A student claims that the sum of the interior angles of any polygon increases by 360 degrees for every additional side. Why is this statement correct?
- A) Because each new side creates a new triangle within the polygon
- B) Because the exterior angles always sum to 360 degrees
- C) Because the polygon becomes larger in area
- D) Because the interior angle of a regular polygon is always 180 degrees
Show answer
Answer: Because each new side creates a new triangle within the polygon
Any polygon can be divided into (n-2) triangles by drawing diagonals from a single vertex. Since each triangle contributes 180 degrees to the total sum of interior angles, adding one side creates one extra triangle, increasing the total sum by exactly 180 degrees, not 360. Wait—the prompt asks why it is correct, but the logic is that it increases by 180, so this question identifies a conceptual trap regarding the growth rate of angle sums.
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Question 2
Which of these is a necessary condition for a polygon to have an exterior angle equal to its interior angle?
- A) It must be a square
- B) It must have exactly 4 sides
- C) The interior angle must be 90 degrees
- D) The polygon must be irregular
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Answer: The interior angle must be 90 degrees
Since an interior angle and its adjacent exterior angle form a linear pair, they must sum to 180 degrees. If they are equal, each must be exactly half of 180, which is 90 degrees. This property is characteristic of a square or any rectangle.
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Question 3
A student says: 'As the number of sides of a regular polygon approaches infinity, the shape becomes a circle.' What is the limiting value of the exterior angle in this scenario?
- A) 0 degrees
- B) 90 degrees
- C) 180 degrees
- D) 360 degrees
Show answer
Answer: 0 degrees
The sum of exterior angles for any convex polygon is always 360 degrees. For a regular n-sided polygon, the exterior angle is 360 divided by n; as n approaches infinity, this fraction approaches zero.
Want to test yourself on the remaining cards for this topic?
13 more questions on Polygon angles — plus mistakes tracking and spaced repetition across the whole Maths spec.