1. ## HELP!!! ratios! ack!!

I reallly wanna go to bed but I need to get my homework done and I'm absolutely stuck on this one.

"The measures of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle."

2. Originally Posted by A dumb person
I reallly wanna go to bed but I need to get my homework done and I'm absolutely stuck on this one.

"The measures of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle."

Let $\alpha$ represent the smaller angle, and let $\beta$ represent the larger angle.

Thus, we see that $\frac{\beta}{\alpha}=\frac{5}{3}$

Now, the larger angle is 30 more than half of the difference of the angles. This means that $\beta=30+\tfrac{1}{2}(\beta-\alpha)$

We can now solve this system of equations:

\left\{\begin{aligned}30+\tfrac{1}{2}(\beta-\alpha)&=\beta\\\tfrac{3}{5}\beta&=\alpha\end{alig ned}\right.

Try to take it from here. It shouldn't be that bad.

I hope this makes sense!

--Chris