My 10th grade teacher gave us geometry homework and this problem has me stumped for sure. This rhombus has three interior angles: (5x-2)°, (8y+2)°, and (3x+22)° .

Question

We are supposed to find the value of x and y. I tried to use an equation by assigning the fourth angle as "z" and all equal to 360° but don't seem to be able to work it out.
Apparently I should break this up into triangles or something but my brain seems to be failing me.
Am I losing my mind?
I can get through the CA State Geometry Standard Test on my own but this teacher has come up with some unusual Core Concepts (grrrrr) things.

I did this - apparently the wrong approach?
(5x-2)°+(8y+2)°+(3x+22)°+z°=360° but when I tried to do this on my computer it changed all the variables to x and came up with x=2 . If I substitute that it gives me a stupid answer for the interior angles. For example one of the acute angles would then be 28° while the other (opposite) would be 8° but these should be equal. And the z obtuse angle (I arbitrarily assigned z to the angle not given in the problem) would be 2° (?). This appears to be an impossible problem because no matter what value x has, the opposite angles will never be equal. What am I missing?
Did the teacher mess up here?
Luis

Answer 1

Assuming the three angles are listed in order, you have to remember that

consecutive angles are supplementary
opposite angles are equal. So,

5x-2 + 8y+2 = 180
5x-2 = 3x+22
So,
x = 12, making y=15