Finding The Measure(s) Of Different Angles

[XxHelpMePlzxX]

I usually am pretty good at these, but it's really late for me, and my ADHD isn't helping. The problem I'm having trouble with is below:

The measures of two angles have the ratio of 5:2. The larger of the angles is 30 more
than half the difference of the angles. Find the measure of each angle.

Thank you so much!
-Zander

 

[Harry_the_cat]

Let the larger angle be X and the smaller angle be Y. Can you come up with 2 equations to solve simultaneously?

 

[The Highlander]

I usually am pretty good at these, but it's really late for me, and my ADHD isn't helping. The problem I'm having trouble with is below:

The measures of two angles have the ratio of 5:2. The larger of the angles is 30 more
than half the difference of the angles. Find the measure of each angle.

Thank you so much!
-Zander

Hi,

Although what "Harry" says (above) is perfectly valid, I would suggest it might be easier to take the larger angle as $\displaystyle y$ and the smaller as $\displaystyle x$ (they do everything upside down in Australia you see ?).

That would then give you: $\displaystyle 5x=2y$ (ie: $\displaystyle 2y=5x$) ‘straight away’ (from the ratio).

To help you out with the other piece of information provided, you should get this:-

$\displaystyle \frac{(y-x)}{2}+30=y\\  \Rightarrow 2y=y-x+60\\\Rightarrow y=60-x$​

Now that you have two equations (of the form $\displaystyle ay=bx+C$) you should be able to solve these simultaneously and come up with values for the measures of each of the angles.

Be warned: the answers will involve improper fractions (or mixed numbers; which would be preferable) involving sevenths (just a wee hint ?).

 

[XxHelpMePlzxX]

Hi,

Although what "Harry" says (above) is perfectly valid, I would suggest it might be easier to take the larger angle as $\displaystyle y$ and the smaller as $\displaystyle x$ (they do everything upside down in Australia you see ?).

That would then give you: $\displaystyle 5x=2y$ (ie: $\displaystyle 2y=5x$) ‘straight away’ (from the ratio).

To help you out with the other piece of information provided, you should get this:-

$\displaystyle \frac{(y-x)}{2}+30=y\\  \Rightarrow 2y=y-x+60\\\Rightarrow y=60-x$​

Now that you have two equations (of the form $\displaystyle ay=bx+C$) you should be able to solve these simultaneously and come up with values for the measures of each of the angles.

Be warned: the answers will involve improper fractions (or mixed numbers; which would be preferable) involving sevenths (just a wee hint ?).

Alright, thank you so much!

 

[The Highlander]

Alright, thank you so much!

Do let us know how you get on.
Post your own working(s) & results?