Question

In a cyclic quadrilateral ABcd it being given that angle a is (x+y+10)° b is (y+20)° c is (x+y-30)° d is (x+y)°

Answer 1

Answer:

In a cyclic quadrilateral ABCD: ∠A = (x + y + 10)° ∠B = (y + 20)° ∠C = (x + y – 30)° ∠D = (x + y)° We have: ∠A + ∠C = 180° and ∠B + ∠D = 180° [Since ABCD is a cyclic quadrilateral] Now, ∠A + ∠C = (x + y + 10)° + (x + y – 30)° = 180° ⇒ 2x + 2y – 20 = 180 ⇒ x + y – 10 = 90 ⇒ x + y = 160 ……(i) Also, ∠B + ∠D = ( y + 20)° + (x + y)° = 180° ⇒ x + 2y + 20 = 180 ⇒ x + 2y = 160 On subtracting (i) from (ii), we get: y = (160 – 100) = 60 On substituting y = 60 in (i), we get: x + 60 = 100 ⇒ x = (100 – 60) = 40 ∴ ∠B = (y + 20)° = (60 + 20)° = 80°Read more on Sarthaks.com - https://www.sarthaks.com/1115809/in-cyclic-quadrilateral-abcd-it-is-being-given-that-a-10-b-y-20-c-30-and-d-then-b?show=1115813

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