Mathematics, 19.10.2019 09:20 21marmong

If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have? 10 12 20 24

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Since the sum of the angles is 360°, we need to divide 360 with the number of sides that a polygon has.
360/18=20; this polygon has 20 sides.
Result:20

Answer from: zionnahl

The polygon has 20 sides (Icosagon)

Step-by-step explanation:

As the smallest angle of rotation for a regular polygon is 18°, so a 18° rotation yields the same figure.

According to the attachment, the side AB subtends an angle of 18° at the centre. That is why a 18° rotation generates the same figure.

According to the properties of regular polygon,

$OA=OB\ \ \Rightarrow m\angle OAB=m\angle OBA$

And

$m\angle OAC=m\angle OAB$

(as the radius of a regular polygon bisects the interior angle)

As in the triangle OAB,

$\Rightarrow m\angle AOB+m\angle OAB+m\angle OBA=180^{\circ}$

$\Rightarrow 18^{\circ}+2m\angle OAB=180^{\circ}$

$\Rightarrow m\angle OAB=81^{\circ}$

So,

$\Rightarrow m\angle CAB=2m\angle OAB=162^{\circ}$

So, interior angle of polygon is 162°

We know that, the interior angle of regular polygon with n side is,

$=\dfrac{(n-2)180}{n}$

Hence,

$\Rightarrow \dfrac{(n-2)180}{n}=162$

$\Rightarrow (n-2)180=162n$

$\Rightarrow 180n-360=162n$

$\Rightarrow 180n-162n=360$

$\Rightarrow 18n=360$

$\Rightarrow n=20$

Therefore, the polygon has 20 sides (Icosagon)

If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have? 1

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

no because after the troops were pulled many blacks were killed by hangings lynchings and other cruel ways which in a way interrupted the reconstruction of the south and differed from the way abraham lincoln had an idea of reconstruction

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