Question

An Oriental rug is 52 years old and a Persian rug is 16 years old. How many
years ago was the Oriental rug four times as old as the Pensian Rug?​

Answer 1

Sum of four angles of a quadrilateral = 360°

Ratio in the angles = 3 : 5 : 9 : 13

Let first angle = 3x

Then second angle = 5x

Third angle = 9x

and fourth angle = 13x

∴ 3x + 5x + 9x+ 13x = 360°

⇒ 30x = 360°

⇒ x = 360∘30 = 12°

∴ First angle = 3x = 3 x 12° = 36°

Second angle = 5x = 5 x 12° = 60°

Third angle = 9x = 9 x 12° = 108°

Fourth angle = 13 x 12° = 156°