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Chapter Overview
Learning Goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Interior and exterior angles refer to specific angles in a shape (or polygon). There are formulae that can be used to calculate the interior and exterior angles of regular polygons.
A polygon is another word to describe a 2D shape.
A regular polygon is a 2D shape that has equal sides and angles.
An interior angle of a polygon is the inner angle formed by two sides of a shape.
An exterior angle of a polygon is the formed by extending one side of the shape past the vertex.
In the diagram above, the angles $\alpha$ and $75\degree$ are internal angles. The angle $135^\circ$ is an external angle.
Note: It is worth noticing that an interior and exterior angle are two angles on a straight line, which means that they add together to make $180\degree$.
The sum of the interior angles of a polygon can be found using the formula:
$\theta=(n-2)\times180$
Where $\theta$ is the sum of the interior angles, and $n$ is the number of sides.
The interior angles of a regular polygon are equal. Therefore, to find the size of one interior angle, divide the value of $\theta$ by the number of sides.
What is the size of an interior angle of a regular nonagon?
A nonagon has $9$ sides, so $n=9$. The sum of the interior angles is therefore given to be:
$\theta=(n-2)\times180=(9-2)\times180=7\times180$
$\theta=1260\degree$
To find the size of one interior angle, divide this number by $9$:
$1260\div9=140$
The size of one interior angle of a nonagon is $\underline{ 140\degree}$.
Exterior angles of a regular polygon always add up to $360\degree$. Therefore, the formula for one exterior angle is given to be:
$\theta=\dfrac{360}{n}$
Where $\theta$ is the size of one exterior angle, and $n$ is the number of sides.
What is the size of one exterior angle of a regular nonagon?
Substitute $n=9$ into the formula to give:
$\theta=\dfrac{360}{9}=40$
The size of one exterior angle of a regular nonagon is $\underline{ 40\degree}$.
Note: Notice how the interior and exterior angle of a regular nonagon adds up to $180\degree$.
Interior and exterior angles refer to specific angles in a shape (or polygon). There are formulae that can be used to calculate the interior and exterior angles of regular polygons.
A polygon is another word to describe a 2D shape.
A regular polygon is a 2D shape that has equal sides and angles.
An interior angle of a polygon is the inner angle formed by two sides of a shape.
An exterior angle of a polygon is the formed by extending one side of the shape past the vertex.
In the diagram above, the angles $\alpha$ and $75\degree$ are internal angles. The angle $135^\circ$ is an external angle.
Note: It is worth noticing that an interior and exterior angle are two angles on a straight line, which means that they add together to make $180\degree$.
The sum of the interior angles of a polygon can be found using the formula:
$\theta=(n-2)\times180$
Where $\theta$ is the sum of the interior angles, and $n$ is the number of sides.
The interior angles of a regular polygon are equal. Therefore, to find the size of one interior angle, divide the value of $\theta$ by the number of sides.
What is the size of an interior angle of a regular nonagon?
A nonagon has $9$ sides, so $n=9$. The sum of the interior angles is therefore given to be:
$\theta=(n-2)\times180=(9-2)\times180=7\times180$
$\theta=1260\degree$
To find the size of one interior angle, divide this number by $9$:
$1260\div9=140$
The size of one interior angle of a nonagon is $\underline{ 140\degree}$.
Exterior angles of a regular polygon always add up to $360\degree$. Therefore, the formula for one exterior angle is given to be:
$\theta=\dfrac{360}{n}$
Where $\theta$ is the size of one exterior angle, and $n$ is the number of sides.
What is the size of one exterior angle of a regular nonagon?
Substitute $n=9$ into the formula to give:
$\theta=\dfrac{360}{9}=40$
The size of one exterior angle of a regular nonagon is $\underline{ 40\degree}$.
Note: Notice how the interior and exterior angle of a regular nonagon adds up to $180\degree$.
Angle rules
FAQs
Question: What is the formula for an exterior angle of a regular polygon?
Answer: The exterior angle of a regular polygon is found by calculating 360/n, where n is the number of sides.
Question: What is the formula for the sum of interior angles?
Answer: The sum of interior angles of a polygon is (n-2)x180, where n is the number of sides.
Question: What are interior and exterior angles?
Answer: An interior angle of a polygon is the inner angle formed by two sides of the shape. An exterior angle of a polygon is the angle formed by extending one of the lines past the vertex.
Theory
Exercises
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