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Question
In the given figure, ABCD is a parallelogram, find the values of x and y.
Solution
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.
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