Finding the angles of a parallelogram.

Question

In a parallelogram, one angle is $2/5th$ of the adjacent angles. Determine the angles of the parallelogram.

I tried the following,

Let the adjacent angles be $2x$

Let the other angle be $y$

Accordingly, $y=6/5*2x$

What should I do next? Please help.

Answer 1

You have the following equations. First, if we call $x$ and $y$ the different angles that you can find in the parallelogram.

$$2x+2y=360$$

And then the relation between $x$ and $y$ reads:

$$\frac{2x}{5}=y$$

You can get the answer from here. I'll give the result so you can check them after solving the equations.

$$x=\frac{900}{7} \qquad y=\frac{360}{7}$$

EDIT: As olive said I'm working in degrees, if you wanted the solution in radians you just have to take into account that $\pi \quad \text{radians}=180º$

Answer 2

In a parallelogram, addition of 2 adjacent angles always produces $\pi$. Can you take it from here?

Also, I think you might have misunderstood the question. If any of the adjacent angles(the angles to the clockwise and the anti-clockwise direction to any angle $\angle A$ are mutually equal) is x, then the angle in question is 2x/5.

What you assumed would probably be true if the question read, "In a parallelogram, one angle is 2/5th of the SUM OF adjacent angles. "

Answer 3

Sum of two adjacent angles in a parallelogram is $180^{\circ}$, so you have $$x + \frac{2x}{5} = 180^{\circ}.$$