The ratio of sides of two regular polygons is 1:2 and the ratio of measures of their interior angles is 3:4 . What is the number of sides ?
Answers
Answered by
2
Answer:
5,10
Step-by-step explanation:
Attachments:
Answered by
0
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.
Step-by-step explanation:
hope helps
Similar questions