Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 3

Which of the following shapes has the most interior angles? Circle your answer. [A] Octagon [B] Heptagon [C] Pentagon [D] Kite?

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Video Transcript

Which of the following shapes has the most interior angles? Circle your answer. Is it octagon, heptagon, pentagon, or kite?

If we firstly consider each of the shapes individually, an octagon has eight sides. Any shape with eight sides will also have eight interior angles, as shown in the diagram. A heptagon has seven sides. This means that it will have seven interior angles, as shown. The third shape was a pentagon. And a pentagon has five sides. As a pentagon has five sides, it will also have five interior angles.

We can go one step further here and say that any polygon will have the same number of interior angles as it has sides. In this case, the octagon had eight sides and eight interior angles. The heptagon had seven sides and seven interior angles. And the pentagon had five sides and five interior angles.

Our final shape is a kite. A kite is a quadrilateral. This means it has four sides. As the kite has four sides, it will once again have four interior angles.

We were asked in the question to find the shape with the most interior angles. The correct answer is the octagon as eight is greater than seven, five, and four. Out of the four shapes, octagon, heptagon, pentagon, and kite, the shape with the most interior angles is the octagon.

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