Welcome to simplemethod11 lesson, in this post I will teach you how to solve different questions on the topic "polygon" The mathematics is one of the most easiest mathematics since the beginning of calculating polygon. This mathematics deals with calculating the interior and exterior side of a shape called polygon.
Sum of interior angles: ((n - 2) x 180
Sum of exterior angles: Always 360
Most students are still getting it hard to calculate interior and exterior angles of a polygon, but this will make it simple for you to understand the concept of this topic. If you are in JS3 and SS2 this lesson is for you.First before you can solve any problem that involves a polygon of any shape you must be familiar with the formulae.
This mathematics is always very simple but some students do not still get to know how is been solve, but this post will help you break everything to your understanding. Now let me teach you how to solve any significant issues concerning this topic.
To find the internal (interior) and exterior angles of a regular polygon with
sides, use these two fundamental geometric formulas:
360
Exterior angles = -------------
n
Interior angles= 180 - interior angles.
The above information is your key to deal with questions given on regular polygon.
1. What is the interior angle of a regular pentagon with 5 sides.
Solution
First, you find the exterior angle
360º
= ----------------
n
360º
= ------------
5
= 72º
Interior angle = 180º - 72º
= 108º
The interior angle is 108º.
Wow! That's amazing, this means anytime you're aske to solve similar problem, divide 360 by any given n side ( n = 5 )
N side means, number of side.
2. What is the exterior angle of a regular octagon ( n = 8)
Solution
360
= --------------
n
360
= -----------
8
= 45º
The above information is a unique answer to all similar problems. That anytime you're aske to fine the exterior angle of a regular polygon, do the same thing and your good to go.
3.Calculate the interior angle of a regular hexagon ( n = 6 )
Solution
360
Exterior angle = -----------
n
360º
= --------------
6
= 60⁰
Interior angle = 180⁰ - 60⁰
= 120⁰
Good! The answer is 120⁰, this simply means, anytime you're ask to solve any significant problems like this, Brainimatic Series encourage you to use the same method. To summerise this, we first find the exterior angle before interior.
4.What is the interior angle of a regular dodecagon ( n = 12)
Solution
With the above method, we can find the interior angle of 12 side of a polygon.
First, we find the exterior angle:
Let x be our interior angle
360⁰
= --------------
n
360⁰
= -------------
12
= 30⁰
Interior angle x = 180⁰ - 30⁰
= 150⁰
This is a direct guides, it can not change, follow the same method and you deal with any of this question.
5. What is the exterior angle of a regular polygon with 15sides? ( n = 15 )
Solution
360º
= ------------------
n
360⁰
= ----------------
15
= 24⁰
The answer is 24⁰ , is well clay that anytime some like this occur you should do the same thing.
If always get hard to fine the angle of a regular polygon, follow my steps and the formula. Once you understand the method, all the problem can be solved when it comes to finding the angle of a regular polygon of any side.
How to find the n - side of a regular polygon ( Finding the Number of Sides ( from n given side)
The next lesson to focus is how we can find the n - side of a particular regular polygon. I so much believe that we can now find any angle of a regular polygon, what about the n - side? . The n - side of a polygon can be found by dividing 360 degree angle the given angle. To be sure, if you are ask to find the number of a regular polygon, you will be given an angle ( x ) . The x represent a number.
1.A regular polygon has an exterior angle of 40⁰ .How many sides does it have?
Solution
Let side be y.
360⁰
= --------------
a
360⁰
= ----------------
40⁰
y = 9
The n side is called " Nonagon"
That is is how to find the n side of a particular regular polygon. If you have the same problem to solve in a game, use the same pattern, it is 100% sure. Let see how we can find the n side an interior polygon with a given angle.
2. If the interior angle of a regular polygon is 144⁰. find its number of sides.
Solution
First we subtract 144 degree by 180 degree since the interior angle is 180 degree
180⁰ - 44⁰ = 36⁰
360⁰
n side = ------------
36⁰
= 10⁰
That's good! You can see how is very simple to find n side of an interior polygon. With this , you can solve similar problem.
3. A regular polygon has an interior angel of 12. What is the name based on its sides?
Solution
360⁰
= ------------
12⁰
= 30⁰
This is called triacontagon
Angle Relationships & Ratios
1.The ratio of an interior angle to an exterior angle of a regular polygon is 3 : 1.Find the exterior angle, hence what is the side of the exterior angle
Solution
Let the exterior angle= x and the interior angle= 3x.
3x + x = 180⁰
4x = 180⁰
Divide both sides by 4.
180⁰
= ------------
4
x = 45⁰
Side of the polygon, remember how to find any side of a regular polygon.
360⁰
= -----------
45⁰
n = 8. Octagon
2.The ratio of an interior angle to an exterior angle of a regular polygon is 4 : 1.Find the interior angle.
Let the exterior angle be 4x and the interior an the interior angle be x 4x
4x + x = 180
5x = 180
x = 36⁰
= 36⁰ x 4
Interior =144⁰
That is how to find n side and the angle of a regular polygon.If some questions based on the lesson, please put them in the comments box.
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