<p>p683 (Practice Test 5, Section 9, #13)</p>
<p>There's a picture of a triangle with the lines extending from the vertices on the outside. The bottom right interior angle is z, the angles supplementary to the VA of the bottom left interior angle are x, and the angles supplementary to the VA of the top interior angle are y degrees. The lines are named to confirm that they are indeed lines.</p>
<p>In the figure above, if z = 30, what is the value of x + y?</p>
<p>Thanks!</p>
<p>Those who know their geometry formulas inside and out can probably answer this question really quickly using some obscure property of triangles and exterior angles. The rest of us have to resort to the following method:</p>
<p>The first thing to notice is that the three angles in the triangle have the following magnitudes, the first two of which are determined using supplementary angles: 180 - x, 180 - y, and 30 (angle Z). Since the sum of these three angles is 180, we have the following equivalence: 180 - x + 180 - y + 30 = 180. Simplifying yields 360 - x - y = 150. "Antidistribution" of a negative sign causes this equation to look like this: 360 - (x+y) = 150...which, simplifying, is equivalent to x + y = 210. Voila!</p>