how to find exterior angles
Angles, lines and polygons
Polygons are multi-sided shapes with different properties. Shapes have symmetrical properties and some can tessellate.
Polygons
A polygon is a 2D shape with at least three sides.
Types of polygon
Polygons can be regular or irregular. If the angles are all equal and all the sides are equal length it is a regular polygon.
Interior angles of polygons
To find the sum of interior angles in a polygon divide the polygon into triangles.
The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.
Example
Calculate the sum of interior angles in a pentagon.
A pentagon contains 3 triangles. The sum of the interior angles is:
\[180 \times 3 = 540^\circ\]
The number of triangles in each polygon is two less than the number of sides.
The formula for calculating the sum of interior angles is:
\((n - 2) \times 180^\circ\) (where \(n\) is the number of sides)
- Question
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Calculate the sum of interior angles in an octagon.
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Using \((n - 2) \times 180^\circ\) where \(n\) is the number of sides:
\[(8 - 2) \times 180 = 1,080^\circ\]
Calculating the interior angles of regular polygons
All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is:
\[\text{interior angle of a polygon} = \text{sum of interior angles} \div \text{number of sides}\]
- Question
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Calculate the size of the interior angle of a regular hexagon .
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The sum of interior angles is \((6 - 2) \times 180 = 720^\circ\) .
One interior angle is \(720 \div 6 = 120^\circ\) .
Exterior angles of polygons
If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle.
The sum of the exterior angles of a polygon is 360°.
Calculating the exterior angles of regular polygons
The formula for calculating the size of an exterior angle is:
\[\text{exterior angle of a polygon} = 360 \div \text{number of sides}\]
Remember the interior and exterior angle add up to 180°.
- Question
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Calculate the size of the exterior and interior angle in a regular pentagon .
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Method 1
The sum of exterior angles is 360°.
The exterior angle is \(360 \div 5 = 72^\circ\) .
The interior and exterior angles add up to 180°.
The interior angle is \(180 - 72 = 108^\circ\) .
Method 2
The sum of interior angles is \((5 - 2) \times 180 = 540^\circ\) .
The interior angle is \(540 \div 5 = 108^\circ\) .
The interior and exterior angles add up to 180°.
The exterior angle is \(180 - 108 = 72^\circ\) .
- The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.
- The formula for calculating the sum of interior angles is \((n - 2) \times 180^\circ\) where \(n\) is the number of sides.
- All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
- The sum of exterior angles of a polygon is 360°.
- The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.
how to find exterior angles
Source: https://www.bbc.co.uk/bitesize/guides/zshb97h/revision/6#:~:text=The%20sum%20of%20exterior%20angles%20of%20a%20polygon%20is%20360,360%20%C3%B7%20number%20of%20sides.
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