The ratio of measure of interior angle of a regular polygon is 8:9 and ratio of their is 3:4 .find the number of sides of the polygon
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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