Question

ABCD is a cyclic quadrilateral. Find the angles of the cylic quadrilateral.
LA = 4y+20, LB = 3y - 5, LC = -4x, LD =-7x+5.
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Answer 1

Answer:

A = 4y + 20 = 154°

B = 3y - 5 = 95.5°

C = -4x = 26°

D = -7x + 5 = 50.5°

Step-by-step explanation:

the opposite angles of a cyclic quadrilateral add up to 180°

=> A + C = 4y + 20 - 4x = 180° ... (1)

and, B + D = 3y - 5 - 7x + 5 = 180° ... (2)

=> from (1), y + 5 - x = 45° ... (4)

=> 3y + 15 - 3x = 135° ... (3)

subtracting (3) from (1), -20 - 10x = 45°

=> 10x = -65°

=> x = -6.5°

substituting the value of x in (4), y + 5 + 6.5 = 45

=> y = 33.5°

=> A = 4y + 20 = 154°

B = 3y - 5 = 95.5°

C = -4x = 26°

D = -7x + 5 = 50.5°