<p><a href="http://i45.tinypic.com/2jd3ql2.jpg%5B/url%5D">http://i45.tinypic.com/2jd3ql2.jpg</a></p>
<p>What is the answer?</p>
<p>The triangle has a total of 180 degrees. The angle right next to the 115 degree angle is 65 degrees because straight lines are also 180 degrees. Knowing that one angle within the triangle is 65 degrees, the other two angles in the triangle total up to 115 degrees. Now you try to find the total degrees of two straight lines minus the parts in the triangle. Soo…</p>
<p>2(180) - 115 = 245 </p>
<p>Answer is e) 245 degrees</p>
<p>This may sound quite stupid, but I just combined the y and z along with the given to form a circle, then I just subtracted 360-115. I’m not sure if that can be done every time. Is 245 the right answer by the way?</p>
<p>I think it’s 245. Y= 115 and Z= 130.</p>
<p>The “triangle” in the diagram will have angles of 65, 180-y, and 180-z. They must add up to 180, so</p>
<p>65 + (180-y) + (180-z) = 180</p>
<p>245 - y - z = 0, adding y+z to both sides we get y+z = 245, E.</p>
<p>Yeah I also got 245, but I did it the long and random way. </p>
<p>I knew that the sum of the two missing angles of the triangle was equal to the extrior angle, or 115. Then (almost like KansasGuy) I pretended that the two angles were 50 and 65 (so that the triangle adds up to 180). Then I filled in y and z as 130 and 115, respectively, because they’re supplementary. Then 130+115=245.</p>
<p>I think I’ll just do 360-115=245 next time. :)</p>
<p>@KansasGuy and qtpiginger, the “guessing” method works for the SAT, but I wouldn’t stick to it, particularly if you’re taking more rigorous math courses, where you have to prove your answer.</p>
<p>The general way is to solve for x+y given (180-x) + (180-y) + 65 = 180. Haphazard suggested an interesting solution; “slide” line m and angle z to form a 360-degree angle with 115+x+y = 360, x+y = 245. That works as well.</p>
<p>Here is one other way to do it. </p>
<p>Use the fact that the measure of an exterior angle to a triangle is the sum of the 2 opposite interior angles of the triangle. Using this you can see that you must add the interior angle at the top twice, and the other 2 interior angles once. In other words, you get 180 + 65 = 245, choice (E).</p>
<p>With this method you can get the answer in about 15 seconds without rushing.</p>