Deriving the sum of interior angles in multiple ways | Maths

Starter quiz

A ______ is a flat (2D), closed figure made up of straight line segments.
- 'polygon' ✓
What is the size of ∠BCD?
- 73° ✓
- 84°
- 95°
- 108°
A hendecagon has 11 sides. The minimum number of triangles that it could be split into is ______.
- '9' ✓
A hexadecagon has 16 sides. Which calculation would find the sum of its interior angles?
- $14 \times 180$ ✓
- $14 \times 360$
- $16 \times 180$
- $16 \times 360$
Angles around a point sum to ______°.
- '360' ✓
Evaluate the expression $20(x − 2)$ when $x=5$ .
- '60' ✓

Each time the number of sides of a polygon increases by 1, the sum of the interior angles increases by ______°.
- '180' ✓
The interior angles in 19-sided polygon sum to 3060°. Therefore the interior angles in a 20-sided polygon sum to ______°.
- '3240' ✓
Which expression can be used to calculate the sum of interior angles in a polygon by substituting $n$ for the number of sides?
- $180n$
- $180n - 2$
- $180(n - 2)$ ✓
- $180n + 2$
- $180(n + 2)$
A triacontagon is a polygon with 30 sides. Which calculation finds the sum of its interior angles?
- $180 \times 30$
- $180 \times (30 - 2)$ ✓
- $180 \times (30 + 2)$
A tetracontagon is a polygon with 40 sides. Its interior angles sum to ______°.
- '6840' ✓
A polygon has interior angles which sum to 720°. The polygon has ______ sides.
- '6' ✓

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Not all vertices of component shapes contribute to the sum of the interior angles of a composite shape.
A numerical sequence can be used to derive the sum of interior angles.
A formula can be derived to find the sum of interior angles.

Interior angles always sum to 180 times the number of component triangles it is split into.

If line segments drawn make new vertices in the polygon, its angles won't contribute to the sum of interior angles in the initial polygon.

Polygon - A polygon is a flat (2D), closed figure made up of straight line segments.
Interior angle - An interior angle is an angle formed inside a polygon by two of its edges.
Sum - The sum is the total when numbers are added together.