Find the value of x and y, whereABCD is a parallelogram.

1.	Find the value of x and y, whereABCD is a parallelogram.
Answer» ong>Answer: x = 14 and y = 8. ABCD is a PARALLELOGRAM. Opposite angles of a parallelogram are equal. ∴ ∠A = ∠C ⇒ 4x + 3y - 6 = 9y + 2 ⇒ 4x - 6y = 8 ⇒ 2x - 3y = 4 ....(i) AB \|\| CD and AD is the transversal. ∴ ∠A + ∠D = 180° ....(Co-interior angles are supplementary) ⇒ (4x + 3y - 6) + (6x + 22) = 180° ⇒ 10x + 3y + 16 = 180° ⇒ 10x + 3y = 164 ....(ii) Adding equations (i) and (ii), we get 12x + = 168 ⇒ x = 14 Substituting the VALUE of x in (i), we get 2 x 14 - 3y = 4 ⇒ 28 - 3y = 4 ⇒ 3y = 24 ⇒ y = 8 Hence, x = 14 and y = 8.

Answer»

ong>Answer:

x = 14 and y = 8.

Opposite angles of a parallelogram are equal.

∴ ∠A = ∠C

⇒ 4x + 3y - 6 = 9y + 2

⇒ 4x - 6y = 8

⇒ 2x - 3y = 4 ....(i)

AB || CD and AD is the transversal.

∴ ∠A + ∠D = 180° ....(Co-interior angles are supplementary)

⇒ (4x + 3y - 6) + (6x + 22) = 180°

⇒ 10x + 3y + 16 = 180°

⇒ 10x + 3y = 164 ....(ii)

Adding equations (i) and (ii), we get

12x + = 168

⇒ x = 14

Substituting the VALUE of x in (i), we get

2 x 14 - 3y = 4

⇒ 28 - 3y = 4

⇒ 3y = 24

⇒ y = 8

Hence, x = 14 and y = 8.

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