We know the length is 90 and width is 30. We need to find the measures of the angles. We also know that the area is 300.
Area of parallelogram = L x h (H is height, not the side length of 30)
We know Area is 300 and L = 90, but we don't know the height. So we can solve for h.
300 = 90h
h = 300/90 = 10/3
Now that we know the height, we can figure out the angles. If you look at Xavier's diagram and the part that he labelled as "angle", that angle is also part of a triangle. That triangle has the height 10/3, same as the parallelogram, and a hypotenuse of 30, which is the other side length of the parallegram. 10/3 is the side opposite to the angle, and 30 is the hypotenuse. From SOH CAH TOA, we can use sine to figure out the angle.
@burhan101
sin(x) = (10/3) / (30) = 10/90 = 1/9
We can use the inverse sine function to find angle x.
x = sin^-1(1/9) = 6.38
Another thing we should is that one obtuse and one acute angle of a parallelogram are supplementary, meaning they add up to 180.
If we know angle x,which is the acute angle is 6.38 degrees, we can subtract this from 180 to find the other angle, let's call it y : 6.38 + y = 180 --> y = 180 - 6.38 = 173.62
Therefore, the two angles x and y are x = 6.38 degrees, y = 173.62 degrees