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)° .
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
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
No, you're not losing your mind! It seems like there might be a misunderstanding or error in the problem given by your teacher. Let's analyze the problem to see if we can find a resolution.
A rhombus is a quadrilateral with four equal sides. In a rhombus, the opposite angles are equal. However, in the given problem, the opposite angles (5x-2)° and (3x+22)° are not equal. This means that the given information is contradictory and does not describe a valid rhombus.
It's possible that there might be some missing or incorrect information in the problem statement. I would recommend double-checking the problem or discussing it with your teacher to clarify any confusion or mistakes. Communication with your teacher is important in such situations to ensure you understand the problem correctly.
In mathematics, it's crucial to check for consistency and logical validity of the given information before attempting to solve a problem. If something doesn't seem right or makes the problem unsolvable, it could be an indication of an error in the problem itself.
Keep up the good work and don't hesitate to seek clarification whenever needed!