Please help me on this prob, it is really hard! for me of course, I really need it urgently

1.) The sum of the measures of two obtuse angles is 215. The sum of the 3/5 of the supplement of the smaller angle and 2/3 of the supplement of the larger angle is 91. Find the measures of the angle.

*note* if 215 wont work out, try using 2/5, I'm not sure because the writing of my classmate is confussing

thanks........

2. Originally Posted by Aussieboy
Please help me on this prob, it is really hard! for me of course, I really need it urgently

1.) The sum of the measures of two obtuse angles is 215. The sum of the 3/5 of the supplement of the smaller angle and 2/3 of the supplement of the larger angle is 91. Find the measures of the angle.

*note* if 215 wont work out, try using 2/5, I'm not sure because the writing of my classmate is confussing

thanks........
Call the first angle A and the second angle B. Let A < B.

We know that
A + B = 215
$\displaystyle \frac{3}{5}(180 - A) + \frac{2}{3}(180 - B) = 91$

The second equation simplifies a bit:
$\displaystyle 108 - \frac{3}{5}A + 120 - \frac{2}{3}B = 91$

$\displaystyle \frac{3}{5}A + \frac{2}{3}B = 137$

The first equation says:
$\displaystyle B = 215 - A$

So inserting this into the second equation gives:
$\displaystyle \frac{3}{5}A + \frac{2}{3}(215 - A) = 137$

$\displaystyle \frac{3}{5}A + \frac{2}{3}(215) - \frac{2}{3}A = 137$

$\displaystyle \left ( \frac{3}{5} - \frac{2}{3} \right ) A + \frac{2}{3}(215) = 137$

$\displaystyle \left ( \frac{9 - 10}{15} \right ) A = - \frac{2}{3}(215) + 137$

$\displaystyle \left ( \frac{ -1}{15} \right ) A = - \frac{2}{3}(215) + 137$

$\displaystyle A = 15 \left ( \frac{2}{3}(215) - 137 \right )$

$\displaystyle A = 2150 - 2055$

$\displaystyle A = 95$ (Which is, in fact, an obtuse angle.)

Thus
$\displaystyle B = 215 - 95 = 120$

So A = 95 degrees and B = 120 degrees.

-Dan