two regular polygons are such that the ratio between their number of sides is 1 ratio 3 and the ratio of the measures of their interior angle is 3 ratio 4 find the number of sides of polygon
Answers
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 values 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
Hence the sides are 5 and 10.
Step-by-step explanation:
Step-by-step explanation:
The ratio of number of sides of two regular polygons is 3:4 and the ratio of measures of their each interior angle is 8:9. What is the sum of the number of diagonals of both the polygons equal to?
Ratio of sides of two regular polygons = 3 : 4
Let sides of first polygon = 3n
and sides of second polygon = 4n
Sum of interior angles of first polygon
= (2 × 3n – 4) × 90° = (6n – 4) × 90°
And sum of interior angle of second polygon
= (2 × 4n – 4) × 90° = (8n – 4) × 90°
∴ ((6n – 4) × 90°)/((8n – 4) × 90°) = 2/3
⇒ (6n – 4)/(8n – 4) = 2/3
⇒ 18n – 12 = 16n – 8
⇒ 18n – 16n = -8 + 12
⇒ 2n = 4
⇒ n = 2
∴ No. of sides of first polygon
= 3n = 3 × 2 = 6
And no. of sides of second polygon
= 4n = 4n × 2 = 8