Sum of exterior angles of any polygon is 360 degrees.
<span>Each exterior angle of a regular polygon = 360/n where n is the number of sides. </span>
<span>So, n = 360/20 = 18. Your answer is D
Hope this helps.</span>
Here, we have been asked to find the order of rotational symmetry of a symmetry of a regular pentagon. First let us learn about rotational symmetry and some basic terms related to it.
1. Rotational Symmetry: -
It is the property a shape has when it looks the same after some rotation by a partial turn. For example: - an equilateral triangle will look the same after a partial rotation of 120∘
2. Centre of rotation: -
The fixed point around which the rotation occurs is called the centre of rotation. For example: - the centre of rotation of a fan is the centre of the fan from which its blade originates.
3. Angle of Rotational Symmetry: -
The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself. For example: - the angle of rotation of an equilateral triangle is 120∘
4. Order of Rotational Symmetry: -
The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. For example: - an equilateral triangle can be rotated 3 times around a full circle, each time at the angle of 120∘
, so its order of rotation will be 3.
In general, a regular polygon having n – sides have ‘n’ lines of symmetry and their order of rotational symmetry is ‘n’.
Now, let us come to the question. We have to find the order of rotational symmetry of a regular pentagon.
We know that a regular pentagon has 5 sides.
<h3> Hence, it will have 5 lines of symmetry and its order of rotational symmetry will be 5.</h3>
For this problem, we have to set up the formula for the equation first. The equation should help us predict how long would it take to reach a life expectancy of 130 years. Let's start by denoting variable to present them in algebraic equations. Let x be the number of decades, while y is the number of years for life expectancy. The base year used here is 2009 with a life expectancy of 80 years. So, we will expect that 80 is a constant in the expression. We will add to this the number of decades multiplied by 5.4, because it stands for 5.4 additional years per decade. When you write this in an equation, it would be
y = 80 + 5.4x
Now, we substitute y=130.
130 = 80 + 5.4x
x = (130 - 80)/5.4
x = 9.259
Therefore, it would take approximately more than 9 decades. Projecting this amount of time from 2009, the year would be:
Projected year = 2009 + 9 decades * (10 years/1 decade)
Projected year = 2101
It would be in year 2101.
Let
v-------> <span> the volume of a sphere
s-------> t</span><span>he surface area of the sphere
r------> </span><span>the radius of the sphere
we know that
v=(4/3)*pi*r</span>³-----> v=(r/3)*4*pi*r²------> equation 1
and
S=4*pi*r²-----> equation 2
substitute equation 2 in equation 1
so
v=(r/3)*4*pi*r²-------> v=(r/3)*s
the answer is
the equation that <span>represents the relationship between these three measures
</span> v=(r/3)*s
I had this question asked before lol