Find angles

Posted January 27th, 2009 by mthom078

$\angle P$ and $\angle Q$ are supplementary
$m (\angle P) =x^2$
$m (\angle Q) =8x$

find each angle

please show me how you worked this problem

Comments

On January 27th, 2009 Structure says:

If they are supplementary then the sum of their measures is 180.

$x^2 + 8x = 180$

$x^2 + 8x - 180 = 0$

$(x - 10)(x + 18) = 0$

$x_1 = 10$
$x_2 = -18$

as x > 0 only x = 10 is a good solution

So:
$m(\angle P) = x^2 = 10^2 = 100$
$m(\angle Q) = 8x = 8 \cdot 10 = 80$