2. In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
Correct option is C) In the given figure, ∠POY=90 ∘ ∠POX+∠POY=180 ∘ ( Linear pair ) ∠POX+90 ∘ =180 ∘ ⇒∠POX=90 ∘ a:b=2:3 Let a=2x ∘ and b=3x ∘ ∠POX=a+b=5x 90 ∘ =5x ⇒x=18 ∘ ∠MOX=b=3x=54 ∘ ∠MOX+∠NOX=180 ∘ ( Linear pair) b+c=180 ∘ 54 ∘ +c=180 ∘ c=180 ∘ −54 ∘ =126 ∘
