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PQRS is a cyclic quadrilateral. Find x + y...
PQRS is a cyclic quadrilateral. Find \(x\) + \(y\)

PQRS is a cyclic quadrilateral. Find x + y

A.

50

B.

60

C.

15

D.

0

Correct answer is D

∠PQR + ∠PSR = 180o (opp. angles of cyclic quad. are supplementary)

⇒ 5x - y + 10 + (-2x + 3y + 145) = 180

⇒ 5x - y + 10 - 2x + 3y + 145 = 180

⇒ 3x + 2y + 155 = 180

⇒ 3x + 2y = 180 - 155

⇒ 3x + 2y = 25 ----- (i)

∠QPS + ∠QRS = 180o (opp. angles of cyclic quad. are supplementary)

⇒ -4x - 7y + 150 + (2x + 8y + 105) = 180

⇒ -4x - 7y + 75 + 2x + 8y + 180 = 180

⇒ -2x + y + 255 = 180

⇒ -2x + y = 180 - 255

⇒ -2x + y = -75 ------- (ii)

y = -75 + 2x -------- (iii)

Substitute (-75 + 2x) for y in equation (i)

⇒ 3x + 2(-75 + 2x) = 25

⇒ 3x - 150 + 4x = 25

⇒ 7x = 25 + 150

⇒ 7x = 175

x=1757=25

From equation (iii)

y = -75 + 2(25) = -75 + 50

y = -25

x + y = 25 + (-25) = 0