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Question
In the following figures, ABCD is a parallelogram.
Find the values of x and y.
Solution
In the figure, ABCD is a parallelogram
∠D = ∠B ...[Since opposite angles are equal.]
6x + 3y - 8 = 7y
6x + 3y - 7y = 8
6x - 4y = 8
2(3x - 2y) = 8
3x - 2y = 4 ...(i)
∠A + ∠B = 180°
4x + 20° + 7y = 180°
4x + 7y = 160° ...(ii)
Multiply by equation (i) × 4 and equation (ii) × 3
12x - 8y = 16
12x + 21y = 480
- - -
- 29y = - 464
y = `(- 464)/(- 29)`
y = 16
Put y = 16 in equation (i)
∴ 3x - 2y = 4
⇒ 3x - 2(16) = 4
⇒ 3x - 32 = 4
⇒ 3x = 4 + 32
⇒ 3x = 36
⇒ x = `36/3`
⇒ x = 12
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