The ratio between the number of sides of two regular polygons
is 1:2. The ratio of the measures of their interior angles is 3:4.
How many sides are there in each polygon?
Answers
Answer:
⇒ The ratio of the sides of two polygon is 1 : 2.
⇒ Let the polygon A have n sides & polygon B have 2n sides.
⇒ The sum of the interior angles of A is (n - 2)×180
∘
= 180
∘
n - 360
∘
⇒ So each interior angle,
⇒
n
180
∘
n−360
∘
--- (1)
⇒ Sum of interior angles of B is (2n - 2)×180
∘
= 360
∘
n - 360
∘
.
⇒
2n
360
∘
n−360
∘
--- (2)
⇒ Now the ratio of the interior angles of A and B.
⇒
n
180
∘
n−360
∘
:
2n
360n
∘
−360
∘
::
4
3
---- [From (1) and (2)]
⇒
360
∘
n−360
∘
360
∘
n−720
∘
=
4
3
⇒
360
∘
n(n−1)
360
∘
(n−2)
=
4
3
⇒ 4n−8=3n−3
∴ n=5 and 2n=10
Thus, the number of sides of each polygon is 5 and 10.
Correct option is
A
5, 10
Answer:
Given :-
Two polygon in which the ratio between their number of sides is 1:2
Ratio of interior angles is 3:4
To find :- side of each polygon
Solution :-
The interior angle of the polygon is given by
( (x-2) /x) *180
Let us take the sides as a and 2a .
Substituting in the above formula, we get
( (a-2) /a) *180/( (2a-2) /2a) *180 =3/4
(a-2) /a*2/(a-1) =3/4
(a-2) /(a-1) =3/4
4a-8=3a-3
= a=5
hope my answer is helpful to you
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