Question

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 ?​

Answer 1

Answer:

5,10

Step-by-step explanation:

Answer 2

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