# Thread: Urgent help needed parallelogram

1. ## Urgent help needed parallelogram

In parallelogram ABCD, angle A is x(x+1) and angle B is 108°. Show your work in finding the value of x

2. Originally Posted by OneidaFL
In parallelogram ABCD, angle A is x(x+1) and angle B is 108°. Show your work in finding the value of x
$\angle{A} = \angle{C}$ and $\angle{B} = \angle{D}$.

Also, the angle sum of a parallelogram is $360^{\circ}$.

Therefore:

$\angle{A} + \angle{B} + \angle{C} + \angle{D} = 360^{\circ}$

$x(x + 1) + 108 + x(x + 1) + 108 = 360$

$2x(x + 1) + 216 = 360$

$2x(x + 1) = 144$

$2x^2 + 2x = 144$

$2x^2 + 2x - 144 = 0$

$x^2 + x - 72 = 0$

$(x + 9)(x - 8) = 0$

$x + 9 = 0$ or $x - 8 = 0$

$x = -9$ or $x = 8$.

Since you can't have a negative angle in a parallelogram, that means $x = 8$.