Chapter 9 : Circle

Example 7. In the given figure,

Find the value of x and y.

Solution:- Here ABCD is a cyclic quadrilateral

Or, 2x + 4⁰ + 4y - 4⁰ = 180⁰

Or, 2x + 4y = 180⁰

Or, x + 2y = 90⁰----------------------------(i)

Also,

Or, x + 10⁰ + 5y + 5⁰ = 180⁰

Or, x + 5y = 180⁰ - 15⁰

Or, x + 5y = 165⁰ --------------------(ii)

Subtracting (i) from (ii) we get

(x + 5y) - (x + 2y) = 165⁰ - 90⁰

3y = 75⁰

from (i) x + 2 X 25⁰ = 90⁰

x = 90⁰ - 50⁰ = 40⁰