<p>Hello! I was having trouble understanding the explanation for Practice Test 4, Section 6, #8. Hopefully someone can clear it up for me? Thanks!</p>
<p>well all the angles in a triangle add up to 180 right? so if your given two angles and your trying to find an unknown one you simply subtract the sum of those angles from 180. So the missing angle of the bottom left triangle is 180-(A+b) and when you distribute the negative thats 180-A-B and the missing angle of the middle triangle is also 180-A-B. notice that a straight line also has a angle measure of 180 and the left side of thee bigger triangle is basically a straight line split into 3 parts, and you already have 2 of them. You know 2 of them now and you need to find the third so you know all three angles in the top triangle(the triangle that contains C). So to find it you do 180-[(180-a-b)+(180-a-b)] or simply 180-2(180-a-b). Simplify and you get 180-(360-2a-2b) and simplify further to get -180+2a+2b. Well again 180 minus the sum of this angle and b has to equal the third angle C. So we do 180-(b+(-180+2a+2b)) and that simplifies to 360-2a-3b which is E. This is a confusing problem so I’m sorry if my explanation wasn’t clear</p>
<p>One of my students pointed out a quicker way: Ignore the lower right-
hand triangle and just focus on the remaining quadrilateral. Like all quadrilaterals, its angles add up to 360. So to get C, go around and subtract the other angles from 360. That takes you straight to the answer, E.</p>
<p>I usually have my students solve this by picking numbers first. Then I will try to help them discover pckeller’s method above by asking what kind of figure they get when they delete that one triangle.</p>
<p>Yes, I agree – for many students, making up numbers is the easiest path. Your algebra has to be reasonably nimble to get it right the way Jake11 did (which is fine). As for “deleting the triangle” - well that is the best. But it requires a flash of insight…I want my students to have backup plans for the times when the flash of insight does not come.</p>
<p>This site is a wonderful resource, but it remains that it is good to remind everyone how easy is to find a number of suggested answers. Be it here in the archives or in outside blogs and websites. </p>
<p>Here’s an example of such answers:</p>
<p>I merely googled Practice Test 4, Section 6, #8 and got this withing a few seconds:</p>
<p>[TestTakers</a> Blue Book Blog: Test 4 Section 6 - #8 (page 595)](<a href=“http://bbb.ttprep.com/2009/12/test-4-section-6-8-page-595.html]TestTakers”>TestTakers Blue Book Blog: Test 4 Section 6 - #8 (page 595))</p>
<p>It beats looking the problem in the blue book! And, most importantly, it helps to check different approaches until one clicks in the head. Every problem has different approaches to the same answer, but one is usually faster for a strong student. This problem is no different.</p>
<p>PS To be clear what I suggest is to google the questions, find a couple of suggestions, and then … come here to discuss and verify the validity of the suggested answers. There are gems out there, but also a lot of garbage. For instance, many answers on “ask yahoo” are plain wrong as the one-eyed leads the blind.</p>