Can u plz help me with geometry?

Question

http://i128.photobucket.com/albums/p199/av611/untitled-3.jpg


Follow the link it deals with a picture THX

Answer 1

Since AD is parallel to BC then angle A + angle B = 180 deg. and also angle C + angle D = 180 deg.

So 9x + 12 + 6y = 180, or 9x + 6y = 168. (i)

Also, 5x + 13y - 10 = 180, or 5x + 13y = 190. (ii)

Multiply both sides of equation (i) by 5 and get 45x + 30y = 840.

Multiply both sides of (ii) by 9 and get 45x + 117y = 1710.

Now subtract: (45x + 117y) - (45x + 30y) = 1710 - 840, or
(45x - 45x) + (117y - 30y) = 0 + 87y = 87y = 870. Then y = 10.

Substitute y = 10 into (ii) and get 5x + 13*10 = 5x + 130 = 190,
or 5x = 60. Then x = 12.

You can check by substituting x = 12 and y = 10 back into the original equations.
9*12 + 12 + 6*10 = 108 + 12 + 60 = 180 (OK!)
5*12 + 13*10 - 10 = 60 + 130 - 10 = 180 (OK again!)

The answer is x = 12 deg. and y = 10 deg.

This means that angle A = 9*12 + 12 = 108 + 12 = 120 deg., angle B = 6*10 = 60 deg., angle C = 5*12 = 60 deg., and angle D = 13*10 - 10= 130-10 = 120, so ABCD really is a parallelogram, but even if AB and CD were not parallel, this method would still work.

Answer 2

I assume that's a parallelogram. Opposite angles of a parallelogram are congruent, so we know that

6y = 5x

and

9x + 12 = 13y - 10

We could solve these simultaneously, or we can remember that adjacent angles are supplementary. In that case, we get:

9x + 12 + 5x = 180

and

6y + 13y - 10 = 180

and those will be a lot easier to solve.

Take your choice.