Question 2 In the given figure, lines XY and MN intersect at O. If ∠POY=90∘ and a:b = 2:3, find c.
Open in App
Solution
Let the common ratio between a and b be x. a = 2x and b = 3x XY is a straight line, rays OM and OP stand on it. ∴∠XOM+∠MOP+∠POY=180∘ b+a+∠POY=180∘ 3x+2x+90∘=180∘ 5x=90∘ x=18∘ a=2x=2×18=36∘ b=3x=3×18=54∘ MN is a straight line. Ray OX stands on it. ∴b+c=180∘ ( Linear pair) 54∘+c=180∘ c=180∘–54∘=126∘ ∴c=126∘