Question

In a Cyclic Quadirilaterl ABCD, if LA = (3x+7y+13), LB = (11x+3y) LC= (9x-y+17) and LD = (4x+5y -12) then the measure of LA *​

Answer 1

LA = (3x+7y+13), LB = (11x+3y) LC= (9x-y+17) and LD = (4x+5y -12)

Since ABCD is a quadrilateral ∠A + ∠B + ∠C + ∠D = 360

3x+7y+13 + 11x+3y + 9x-y+17 + 4x+5y -12

27x + 14y + 28 = 360

Since ABCD is cyclic ∠A + ∠C = ∠B + ∠D = 180 °

11x+3y + 4x+5y -12 = 180

15x + 8y = 192

3x+7y+13 + 9x-y+17 = 180

12x + 6y = 150

Cross multiplication => (15*6)x + (8*6)y - (12*8)x - (6*8)y = (192*6) - (150*8)

90x - 96x + 48y - 48 y = 1152 - 1200

-48 = -6x

x = 8

Substituting => 12*8 + 6y = 150

96 + 6y = 150

6y = 54

y = 9

∠A = 3*8 + 7*9 + 13

= 24 + 63+ 13

∠A = 100 °

:-)