MathDB

44

Part of 1957 AMC 12/AHSME

Problems(1)

Angle Chasing in a Triangle

Source:

6/8/2009
In triangle ABC ABC, AC \equal{} CD and \angle CAB \minus{} \angle ABC \equal{} 30^\circ. Then ∠BAD \angle BAD is: [asy]defaultpen(linewidth(.8pt)); unitsize(2.5cm); pair A = origin; pair B = (2,0); pair C = (0.5,0.75); pair D = midpoint(C--B);
draw(A--B--C--cycle); draw(A--D);
label("AA",A,SW); label("BB",B,SE); label("CC",C,N); label("DD",D,NE);[/asy]<spanclass=′latex−bold′>(A)</span> 30∘<spanclass=′latex−bold′>(B)</span> 20∘<spanclass=′latex−bold′>(C)</span> 2212∘<spanclass=′latex−bold′>(D)</span> 10∘<spanclass=′latex−bold′>(E)</span> 15∘ <span class='latex-bold'>(A)</span>\ 30^\circ\qquad <span class='latex-bold'>(B)</span>\ 20^\circ\qquad <span class='latex-bold'>(C)</span>\ 22\frac {1}{2}^\circ\qquad <span class='latex-bold'>(D)</span>\ 10^\circ\qquad <span class='latex-bold'>(E)</span>\ 15^\circ