<p>Page 473 #8</p>
<p>(figure in book)</p>
<li> In the figure above what is the value of c in terms of a and b</li>
</ol>
<p>a. a+3b-180
b. 2a+2b-180
c. 180-a-b
d. 360-a-b
e. 360-2a-3b</p>
<p>I remember this one, don't even have to look at the picture. The answer is E. You can make it really complicated. The triangle in which C is in has another angle that is not B or C. The other angles with A and B in them are 180-a-b. There are two of them. So you find the 3rd angle in the C Triangle by doing 180 - 2(180-a-b). Then you say that C=180-b-(whatever 180-2(180-a-b) was. </p>
<p>This question got way too complicated and took way too long for me. I got the right answer, but I lost a lot of time. You know you could have done to do it in less than in a minute? You won't believe how easy this is: plug in #s for A and B. Let's say that A is 60, B is 60, so that makes the 3rd angle in Triangle C 60. So since that 3rd angle in Triangle C(triangle with C in it) is 60 and B is 60, C=60. Now just plug in 60 for A and B in each of those choices to find that E is the right answer. The key is also to pick #s that work. You don't want to pick #s like A=20 and B=30 because then I don't think it works out correctly. Just pick equal #s, make them all equilaterals, every angle is 60 degrees then.</p>
<p>Doesn't the simple method narrow it down to C and E?</p>
<p>I still don't understand the complicated method. Your description of the picture is correct, except that there is a 4th triangle without any angle labeled.</p>
<p>I know this is probably wrong, but I assumed the two triangles with angles labeled A and B formed a paralellogram, with two equilateral triangles... and then used supplementary and complementary angles to determine that C = B. Then, I looked at the proportion of A to B and confirmed by plug-n-play... A = 72, B = 54, and C = 54.</p>
<p>Where did I go wrong? And I still don't understand the simple method.</p>
I know that this was in 2008, but just to answer your question, I just solved this problem 5 minutes ago
the angel that wasnt labeled and equals 180-c-b also equals 180-360+2a+2b
then 180-360+2a+2b+c+b=180
you simplfy to find c
it took me a while to find too, but I wouldn’t recommend plugging in numbers, because it doesn’t always work.
Let’s do a bit of gravedigging, shall we? 
In the second BB edition this question is on page 595.
At first look it seems the solution should be based on the fact that three angels in a triangle have together 180 degrees. There are plenty of triangles to work with, but when taking a look at the diagram from afar, we may notice that there is also a quadrilateral lurking in there with a sum of its angles adding to 360 deg:
a+(b+b)+(a+c)+b = 360,
2a+3b+c = 360,
c = 360-2a-3b.
I don’t see why plugging in numbers would not work.
Let a=70, b=60.
In each of the two bottom adjacent triangles
180-70-60=50.
For the three supplemental angles
180-50-50=80.
In the top triangle
80+60+c=180,
c=40.
Plugging a and b values in all five answers proves that only E fits:
360-2(70)-3(60) = 40.