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Question

The angles of a cyclic quadrilateral ABCD are <A = 6x + 10 , <B = 5x , <C =  x + y and <D = 3y - 10 . find all the angles of the cyclic quadrilateral


Solution

According to the problem, 6x + 10 + x + y = 180 or, 7x + y = 170 or, y = 170 - 7x Again, 5x + 3y - 10 = 180 or, 5x + 3y = 190 or, 5x + 3(170-7x) = 190 or, 5x + 510 - 21x = 190 or, -16x = -320 or, x = 20 So, y = 170 - 7x = 170 - 140 = 30 So, measure of all angles are 130°, 100°, 50°, 80°

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