# Generalising and comparing generalisations

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## Lesson details

### Key learning points

- In this lesson, we will combine everything learnt so far about angles in polygons to compare how specific examples relate to generalised cases.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 5 Questions

Q1.

The mean interior angle of a quadrilateral is...

180 degrees

360 degrees

45 degrees

Q2.

The mean exterior angle of a pentagon is...

108 degrees

360 degrees

60 degrees

Q3.

If I have a regular polygon with an exterior angle of 5 degrees, how many sides does my polygon have?

36 sides

5 sides

50 sides

Q4.

A square would have both an interior and exterior angle of 90 degrees

False

Q5.

If I had a shape with 180 sides, what would the mean exterior angle be?

180 degrees

3 degrees

4 degrees

### 5 Questions

Q1.

The exterior angles of a hexagon sum to 540 degrees.

True

Q2.

A triangle ALWAYS has each exterior angle as 60 degrees.

True

Q3.

The general formula for working out the mean exterior angle of an n-sided polygon is...

180(n-2)

360

n/360

Q4.

The calculation to work out the sum of the interior angles for an octagon would be...

180 x n

360 x

360(8 - 2)

Q5.

180n - 360 is a generalisation that tells us the...

Sum of the angles around a point

Sum of the angles on a straight line

Sum of the total exterior angles of a polygon