NCERT Class 9 Maths Chapter 6 Lines and Angles Solutions
NCERT Class 9 Maths Chapter 6 Lines and Angles Solutions Exercise 6.1 Q.1. In figure, lines AB and CD intersect at 0. If ∠ AOC + ∠ BOE = 70⁰and ∠ BOD = 40⁰ , find ∠ BOE and reflex ∠COE. Ans: Lines AB and CD intersect at O ∴ ∠ AOC + ∠ BOD | Vertically Opposite Angles But ∠ BOD = 40⁰ , …. (1) | Given ∠ AOC = 40⁰ …(2) Now, ∠ AOC + ∠BOE = 70⁰ ⇒ 40⁰ + ∠ BOE = 70⁰ | Using (2) ⇒ ∠ BOE = 70⁰ – 40⁰ ⇒ ∠ BOE = 30⁰ Again, Reflex ∠COE =∠COD + ∠ BOD + ∠BOE = ∠ COD + 40⁰ + 30⁰ | Using (1) and (2) = 180⁰ + 40⁰ + 30⁰ ∴ Ray OA stands on line CD = 250⁰ (Linear Pair Axiom) Q.2. In figure, lines XT and MN intersect at 0. If⇒∠POY=90⁰ and a:b = 2:3, find c. Ans: Ray OP stands on line XY ∴ ∠POX + ∠POY = 180⁰ | Linear Pair Axioms ⇒ ∠POX +90⁰ = 180⁰ |∵∠POY=90⁰(Given) ⇒ ∠POX = 180⁰-90⁰ ⇒ ∠POX = 90⁰ ⇒ ∠POM + ∠XOM = 90⁰ ⇒ a+b=90 ….(1) A:b = 2:3 ⇒ a = 2k B = 3k Putting the values of a and b in (1), we get 2k + 3k = 90⁰ ⇒ k=18⁰...