Question

Q.30 Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of
their interior angels is 3:4. Find the number of sides of each polygon.
दो समबहुभुजों की भुजाओं की संख्या का अनुपात 1:2 है तथा उनके अंतःकोणों का अनुपात 34 है। प्रत्येक बहुभुज की भुजाओं की संख्या ज्ञात
करें।​

Answer 1

Answer:

Ratio of side’s two polygons = x : 2x

As we know,

Each interior angles of having n sides = [2 (n – 2)] /n × 90

According to the question

⇒ (x – 2) / (x – 1) = 3/4

⇒ 4x – 8 = 3x – 3

⇒ x = 5

Sides of two polygons are 5 and 10.

Short Trick:

Using option

Let the sides of two polygons are 5 and 10, then

Each exterior angles of first polygon = (2 × 3 × 90) /5

Each exterior angles of second polygon = (2 × 8 × 90) /10

Ratio = (2 × 3 × 90) /5 : (2 × 8 × 90) /10 = 3 : 4 (satisfied)

Step-by-step explanation:

Hope this helps