The angles P, Q,

Given: Angles of a quadrilateral are in the ratio 1: 3: 7: 9

Formula Used: Sum of the angles of a quadrilateral = 360⁰

Let the angles be x, 3x, 7x, and 9x

Adding the angles we get,

x + 3x + 7x + 9x = 360⁰

⇒ 20x = 360⁰

⇒ x = 18⁰

So, we have,

x = 18⁰

3x = 54⁰

7x = 126⁰

9x = 162⁰

Angles P, Q, R and S = 18⁰, 54⁰, 126⁰ & 162⁰

∠ P ,∠S & ∠Q, ∠R are supplementary

So, PQ ||RS and it’s a trapezium