MathDB

6

Part of 1987 AMC 12/AHSME

Problems(1)

1987 AMC 12 #6 - Triangle Angle Chasing

Source:

12/31/2011
In the △ABC\triangle ABC shown, DD is some interior point, and x,y,z,wx, y, z, w are the measures of angles in degrees. Solve for xx in terms of y,zy, z and ww. [asy] draw((0,0)--(10,0)--(2,7)--cycle); draw((0,0)--(4,3)--(10,0)); label("A", (0,0), SW); label("B", (10,0), SE); label("C", (2,7), W); label("D", (4,3), N); label("x", (2.25,6)); label("y", (1.5,2), SW); label("zz", (7.88,1.5)); label("w", (4,2.85), S); [/asy] <spanclass=′latex−bold′>(A)</span> w−y−z<spanclass=′latex−bold′>(B)</span> w−2y−2z<spanclass=′latex−bold′>(C)</span> 180−w−y−z<spanclass=′latex−bold′>(D)</span> 2w−y−z<spanclass=′latex−bold′>(E)</span> 180−w+y+z <span class='latex-bold'>(A)</span>\ w-y-z \qquad<span class='latex-bold'>(B)</span>\ w-2y-2z \qquad<span class='latex-bold'>(C)</span>\ 180-w-y-z \\ \qquad<span class='latex-bold'>(D)</span>\ 2w-y-z \qquad<span class='latex-bold'>(E)</span>\ 180-w+y+z
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